International Journal of Analysis and Applications

New Properties of Generalized Fusion Frames in Hilbert \(C^∗\)-Modules

2026-01-03T00:37:42+08:00

In this paper, we provide some generalizations of the concept of fusion frames following that evaluate their representability via a linear operator in Hilbert \(C^*\)-modules. We assume that \(\Upsilon _\xi\) is self-adjoint and \(\Upsilon _\xi(\frak{N} _\xi)= \frak{N} _\xi\) for all \(\xi \in \mathfrak{S}\), and show that if a \(g-\)fusion frame \(\{(\frak{N} _\xi, \Upsilon _\xi)\}_{\xi \in \mathfrak{S}}\) is represented via a linear operator \(\mathcal{T}\) on \(\hbox{span} \{\frak{N} _\xi\}_{ \xi \in \mathfrak{S}}\), then \(\mathcal{T}\) is bounded. Moreover, if \(\{(\frak{N} _\xi, \Upsilon _\xi)\}_{\xi \in \mathfrak{S}}\) is a tight \(g-\)fusion frame, then \(\Upsilon_\xi \) is not represented via an invertible linear operator on \(\hbox{span}\{\frak{N} _\xi\}_{\xi \in \mathfrak{S}}\), We show that, under certain conditions, a linear operator may also be used to express the perturbation of representable fusion frames. Finally, we investigate the stability of this type of fusion frames.

Investigating the Relationships Between Weyl's and Cartan's \(2^{th}\) Curvature Tensors in Finsler Spaces

2025-12-28T02:40:34+08:00

This study investigates the interconnection between Weyl's curvature tensor \(W_{jkh}^i\) and Cartan's second curvature tensor \(P_{jkh}^i\) in the frame of Finsler geometry (or \(F\)-geometry), a broader framework that generalizes Riemannian geometry(or \(R\)-geometry). When describing the curvature characteristics of \(F\)-space which are crucial for simulating a variety of physical events both tensors are crucial. Even though the geometric meanings and physical consequences of these tensors have been thoroughly investigated, their interconnection remains an open area for research. In the present work, we demonstrate that the Weyl's and Cartan's second curvature tensors are connected by a novel set of identities and inequalities that we deduce by examining their algebraic and geometric characteristics. A series of theorems that outline particular circumstances in which the tensors exhibit generalized birecurrent behavior in Finsler spaces (or \(F\)-spaces) are presented. In addition to offering further insight into how these notions are applied in physics, especially in the gravitational field and cosmology, these results are anticipated to improve our knowledge of the curvature structure in \(F\)-spaces and yield interesting findings in the frame of differential geometry and its physical applications.

Fixed Point Theorems in Interpolative G-Metric Spaces: A Novel Approach

2025-11-22T15:34:39+08:00

In this paper, we have introduced a new notion of interpolative G-metric space. We establish a fixed point theorem for a contractive mapping in interpolative G-metric space. Some examples are also provided to illustrate the validity of the result. The presented theorem extends, generalizes and refines various existing results from the literature. As an application we present a model to establish convergence in group decision making.

Interval-Valued Intuitionistic (T, S)-Fuzzy Subsemirings in Semirings

2025-12-22T11:02:23+08:00

In this paper, we introduce the notion of an interval-valued intuitionistic (T, S)-fuzzy subsemirings and investigate some of the properties. Finally, we study under homomorphism, anti-homomorphism and prove some results on these.

The Influence of ESG Practices on Bank Credit: The Moderating Role of Climate Policy Across Countries

2025-12-12T12:00:52+08:00

This paper investigates how banks’ Environmental, Social and Governance (ESG) performance interacts with national climate policy to shape bank credit, as measured by net loans. Using an unbalanced panel of 389 listed commercial banks from multiple countries over the period 2010–2023, we combine bank- level ESG and financial data with the Climate Change Performance Index (CCPI), a synthetic indicator of the ambition and effectiveness of national climate policy. The results of the two-step System-GMM show that, on average, stronger ESG performance and stricter climate policy are associated with a more cautious expansion of net loans. However, the positive, statistically significant interaction between ESG and CCPI indicates that the adverse baseline effect is attenuated as climate policy becomes more ambitious. Overall, the findings suggest that ESG alone is not a sufficient driver of green credit; its effectiveness as a conduit for sustainable lending critically depends on the broader climate policy framework.

Some Singular Value Inequalities for Convex Functions of Matrices

2025-12-25T05:13:20+08:00

In this paper, we obtain some upper bounds for singular value inequalities for convex functions of matrices. Some applications involving the spectral norm and numerical radii of matrices were given. Among other inequalities, we prove that for \(A,B\in \mathcal{\mathbb{M}}_{n}\mathcal{\mathbb{(C)}}\) and for any nonnegative increasing convex function \(f\) on \([0,\infty )\) with \(f(0)=0,\) we have\[
\begin{aligned}
&s_j\!\left(f(|aA^*B+bB^*A|)\right)
\le \tfrac12 \Big[
s_j\!\left(f(a|A|^2+b|B|^2)
\oplus f(b|A|^2+a|B|^2)\right) \\
&\quad +\, s_{j-i+1}\!\left(
f(|bA^*B+aB^*A|)
\oplus f(|aA^*B+bB^*A|)
\right)
\Big],
\end{aligned}
\]where \(a,b\geq 0\) and \(j=1,...,n.\) Also, an upper bound for \(\left\Vert {Re}A\right\Vert \) were given.

Linear Diophantine Type-2 Fuzzy Sets with Applications

2025-12-31T23:14:47+08:00

This article proposes the conventional definition and real life based applications of linear Diophantine type-2 fuzzy sets (LDT2FS), manifesting its supremacy over common fuzzy models. LDT2FS is a new mathematical framework that can address the drawbacks of existing fuzzy sets. As common fuzzy systems, however, these models hold restrictions on acceptance and rejection grades, limiting the flexibility of decision-makers in managing uncertainty. LDT2FS extends the previous study by relaxing these limitations, as decision-makers can specify grades-freely with reference parameters in practice in cases where decision making under uncertainty is necessary when functional relationships are unknown, or when data contain high levels of imprecision. To this end, the less demanding structure of LDT2FS allows for establishing the fit to allow dealing with these uncertainties in an efficient way. It also describes basic arithmetic operations on LDT2FS such as union, intersection, complement, containment, etc. along with their algebraic characteristics. Furthermore, two new operators, the Certainty Operator, and Feasibility Operator, are proposed to convert an LDT2FS into a conventional fuzzy set, simplifying mathematical processing and applications. This article proposes Haming Distance and Euclidean Distance commonly used in pattern recognition, clustering, and classification problems to quantify the differences or similarity between LDT2FS instances.

Optimal Difference Formulas for an Approximate Solution of the Cauchy Problem

2025-12-17T16:44:06+08:00

The key properties of numerical methods for solving ordinary differential equations are determined by their accuracy and stability. The step size is selected based on the accuracy of the numerical solution. In this paper, we will consider difference methods for the approximate solution of first-order ordinary differential equations. Here, we will find the square of the norm of the error functional of difference formulas. To obtain optimal coefficients, we will construct and analyze systems of linear algebraic equations. By solving this system, we will find the optimal coefficients of the difference formulas for specific spaces, and here we will calculate the square of the norm of the error functionals of the optimal difference formulas.

Analysis of Existence, Uniqueness, Stability and Controllability in Pantograph with Caputo–Hadamard Volterra–Fredholm Fractional Integro–Differential Equations

2026-01-06T20:06:06+08:00

This study addresses the analytical verification that a solution exists and that it is uniquely determined Boundary value problems involving the Caputo–Hadamard fractional operator that contain nonlinear Volterra–Fredholm type integrals and pantograph-type arguments under nonlocal boundary conditions, by making use of strategies that involve constructing upper and lower solutions. By converting the fractional differential equations into an equivalent integral form, a nonlinear operator is defined in a Banach space. Existence of a solution is shown through a fixed point theorem (FPT) argument, and uniqueness is obtained by applying the Banach fixed point theorem under suitable assumptions. The stability of the system is examined in the Ulam–Hyers sense, and controllability is verified using an appropriate fixed point framework. A illustrating example is provided to exhibit the practical relevance of the theoretical results.

Intuitionistic Fuzzy Best-Worst Method for Multi-Criteria Decision Making with Application in Health Care Resource Allocation

2025-10-25T16:25:45+08:00

In the health care industry, decision-making is critical for determining the most efficient use of limited resources. Multi-criteria decision-making is a significant area that has been used to solve complex problems. To construct an accurate, adaptable, and sustainable framework for decision-making, an intuitionistic fuzzy best-worst method for multi-criteria decision-making in healthcare resource allocation is being developed. To understand the resource allocation mechanisms in different hospitals, the proposed methods employ a pairwise comparison of seven main criteria: infrastructure, consultancy time, paramedics, hospital stay, healthcare resource allocation, healthcare professionals’ satisfaction, and improvements in resource allocation. The weights calculated from the intuitionistic fuzzy best-worst method indicate that health professional satisfaction is the best criterion, whereas the consultancy time is the worst. The goal of this approach is to effectively handle the inherent ambiguity, complexity, and uncertainty that define problems with healthcare resource allocation. This methodology has a wide range of applications, including: hospital resource management, prioritizing patient care during peak times or emergencies such as pandemics, budgeting and financial planning, evaluating the cost-effectiveness of new treatments or technologies, public health planning, planning and executing community health interventions, strategic planning, and policy making.

Structural Properties and Applications of Generalized Fractional Multivariate q-Laguerre Polynomials

2025-12-26T23:51:57+08:00

We introduce and develop a new class of Generalized Multivariate Fractional q-Laguerre Polynomials (GMFQLP), extending classical q-Laguerre families into a fractional and multivariate setting. Rigorous proofs are provided for generating functions, operational identities, and fractional q-difference equations. Explicit fractional q-integral operators are defined and analyzed. Applications to orthogonality, asymptotics, and Volterra-type integral equations are established. Numerical and graphical results are presented for zeros and structural patterns. This work unifies several existing theories and provides new avenues for quantum calculus and approximation theory.

Almost Near \(\tau^\star(\sigma_1,\sigma_2)\)-Continuity for Multifunctions

2025-12-12T12:46:23+08:00

This paper presents a new concept of continuous multifunctions defined between an ideal topological space and a bitopological space, called almost nearly \(\tau^\star(\sigma_1,\sigma_2)\)-continuous multifunctions. Moreover, several characterizations and some properties concerning almost nearly \(\tau^\star(\sigma_1,\sigma_2)\)-continuous multifunctions are established.

Generalized Kernel Sets via Ideals and the \(\widetilde{\Lambda}\)-Operator

2026-01-03T22:17:57+08:00

This work focuses on examining the properties of the co-local function set as defined in [1]. We define an operator \(\widetilde{\Lambda}\) using co-local function set and investigate its various fundamental properties. Also, we introduce the notion of compatible kernel topology via ideal and obtain its characterizations along with several properties.

Numerical Simulation of a Fractional SEIHRD Epidemic Model Using Adams-Bashforth-Moulton Method

2025-08-14T17:25:29+08:00

Epidemics are infectious diseases that spread rapidly and affect large portions of the population within a specific region and timeframe. Throughout history, such outbreaks have caused devastating impacts on humanity from the Black Death, which eliminated one-third of Europe’s population during the Middle Ages, to the Spanish flu, which claimed millions of lives in the early 20th century. While treatment and prevention strategies vary depending on the nature of the disease, common measures often include quarantine, isolation, improved hygiene, and the development of vaccines and medications. In this study, we propose a hypothetical fractional-order epidemic model to investigate the potential spread of the Ebola virus during the Ramadan season of 2025. The model specifically considers the influx of pilgrims into the Kingdom of Saudi Arabia, one of the world’s leading destinations for religious tourism during Ramadan. We numerically solve the model using the Adams–Bashforth–Moulton Predictor–Corrector Method, and conduct a detailed analysis of the simulation results to better understand the dynamics of the outbreak and propose effective mitigation strategies.

Touchard Polynomials and the Identified New Subclass of Analytic Functions

2025-11-15T20:18:35+08:00

A new analytic function, which includes Touchard polynomials, is presented here as part of this work. Subsequently, we endeavour to derive appraisals for the |d₂|, |d₃| Maclaurin coefficients with respect to this particular subfamily, as well as the Fekete-Szegö functional problem that is associated with it. Moreover, by elaborating on the parameters that were utilised in our primary findings, a multitude of new results are demonstrated below.

An Application of Neutrix Calculus to Modified Degenerate Gamma Function

2025-11-14T15:55:53+08:00

The modified degenerate Gamma function \(\Gamma^{*}\lambda(x)\) is defined for positive values of x; however, it is not defined for zero or negative values of \(x\). In this study, the concepts of neutrix and neutrix limit are employed to extend the definition of the modified degenerate Gamma function \(\Gamma^{*}\lambda(x)\) for all real values of \(x\). The results demonstrate that the established definitions and findings recover the classical results for Euler’s Gamma function \(\Gamma(x)\) as \(\lambda \rightarrow 0\) for all real values of \(x\). Additionally, explicit equations for \(\Gamma^{*}\lambda(0)\) and \(\Gamma^{*}_\lambda(-n)\), where n is a positive integer, are given.

Phase and Norm Retrieval via Projections in 2-Inner Product Spaces

2025-05-01T23:26:14+08:00

This paper introduces and studies 2-phase retrieval and 2-norm retrieval in the context of 2-inner product spaces, generalizing classical phase and norm retrieval problems to a nonlinear geometric setting. A collection of subspaces \(\{W_i\}_{i=1}^M\) in a 2-inner product space \(V\) is said to yield {2-phase retrieval} if the 2-norms of projections \(\|P_i s\|_z = \|P_i b\|_z\) for all \(i\) and all reference vectors \(z \in V \setminus \{0\}\) imply that \(s\) and \(b\) are phase-equivalent (i.e., \(s = c b\) for some scalar \(c\) with \(|c| = 1\)). Similarly, \(\{W_i\}_{i=1}^M\) achieves 2-norm retrieval if the 2-norms \(\|P_i s\|_z\) uniquely determine the 2-norm \(\|s\|_z\) for all \(s \in V\) and all \(z\).

Cross-Lingual Speech Emotion Recognition with Attention-Driven Bi-LSTM: Advancing Kashmiri and Multilingual Adaptation

2025-10-18T20:33:18+08:00

Speech Emotion Recognition (SER) has achieved notable success in high-resource languages, yet remains underexplored for Kashmiri, a low-resource Dardic language characterized by tonal and prosodic complexity. This study introduces the first systematic framework for Kashmiri SER and examines its cross-lingual adaptability using Urdu, Persian, and English language datasets. A Bidirectional Long Short-Term Memory (Bi-LSTM) network with attention mechanism was employed to capture bidirectional temporal dependencies while emphasizing emotionally salient segments, with Mel-Frequency Cepstral Coefficients (MFCCs) and spectrogram features as inputs. Three experiments were conducted: within-language evaluation yielded high accuracies (93.2% for Kashmiri, 97% for Urdu, 85% for Persian, and 80.05% for English); cross-lingual transfer revealed substantial performance decline (25–34%), highlighting phonetic and prosodic mismatches; and progressive domain adaptation improved results up to 89%, 81%, and 83% for Urdu, Persian, and English, respectively. These findings demonstrate the challenges of direct transfer and the promise of adaptation, offering a pathway toward resource-efficient, multilingual SER for underrepresented languages.

Fixed Point Theorem for Interpolative Contraction of Reich-Rus-Ciri´c type Mappings in CAT(0) Spaces

2025-11-09T12:32:52+08:00

In this paper, we present a new fixed point theorem for mappings defined on complete CAT(0) spaces. Specifically, we introduce an enhanced version of the Suzuki-type interpolative Reich–Rus–Čirić contraction that incorporates a geodesic iteration condition reflecting the nonpositive curvature structure of CAT(0) spaces. Our main result ensures the existence and uniqueness of a fixed point under suitable contractive conditions and orbital admissibility. The proof relies heavily on the convexity properties of the metric in CAT(0) spaces and the geometrical behavior of iterative sequences along geodesics. This contributes to the ongoing development of fixed point theory in nonlinear and curved metric settings.

A New Family of Efficient Open-Type Quadrature for the Approximation of Riemann-Stieltjes Integrals Using Derivatives

2025-12-11T01:05:44+08:00

Most of the difficulties in control theory and probability distributions are described in terms of the Riemann-Stieltjes (RS) integral rather than the standard Riemann integral (RI). Numerical approximations for the approximation of the RS integral are required due to the nonlinearity of the integrand and the complexity of the analytical process. The numerical techniques, besides convergence features, should also be computationally effective and time-efficient. In this study, some time-efficient and cost effective numerical approaches for approximating the RS integral are proposed. The proposed approximations are based on Newton-Cotes' standard open-type schemes. We derive derivative-based open Newton-Cotes quadrature schemes in both basic and composite forms, as well as the error terms for the Riemann-Stieltjes integral's numerical evaluation. For the suggested schemes, theorems associated with the degree of precision and order of accuracy are studied with proofs. For all suggested and current rules on the test integrals, the absolute error distributions, computational costs, execution times, and computational orders of accuracy have been calculated. To demonstrate the efficacy of the proposed approaches, a numerical verification method will be used. MATLAB R2022a software was used to achieve the results. The proposed method's quick convergence and high efficacy over the current methods have been demonstrated by the results and theoretical properties.

The Impact of Online Customer Experience on Repurchase Intention in the Context of Digital Transformation and the Prevalence of AI/Chatbots

2025-09-21T23:39:29+08:00

This study aims to explore the impact of various aspects of online customer experience on trust, satisfaction, and repurchase intention in the context of digital transformation. Data were collected from 466 valid survey responses and analyzed using SPSS and SmartPLS. The findings indicate that components of online customer experience, including aesthetic experience, customer experience with online employees, community experience, user experience with ai chatbots, and personalized online experience, all exert positive effects on trust and satisfaction, which serve as critical mediators that foster repurchase intention. Notably, the study highlights the prominent role of advanced technological factors such as AI chatbots and personalization in enhancing the quality of digital experiences. These insights not only contribute to updating the theoretical framework of consumer behavior in online environments but also provide valuable implications for both academic research and marketing practice in the era of artificial intelligence.

Numerical Simulation of Phycoremediation for Nutrient Removal Using the Extended Monod Model with Saulyev Technique

2025-09-28T23:11:23+08:00

Nowadays, as water pollution is increasing from agricultural sectors due to nitrogen and phosphorus, phycoremediation is used to remove nutrients with microalgae. In this paper, a mathematical model is developed to use the extended Monod model to analyze the growth of microalgae that have adsorbed nutrients by considering various flow velocities and levels of nitrogen as effects of biomass concentration. This model has been calculated with the numerical finite difference method using the Saulyev technique. Numerical simulations show results for various scenarios with flow velocities and levels of nitrogen that affect the growth of microalgae.

Applying Quadri-Partition Neutrosophic Soft Locally Compact Spaces to Enhance Machine Learning and Uncertainty Management

2025-09-16T23:57:11+08:00

Within the broader framework of quadri-partition neutrosophic soft bi-topological spaces (QPNSBTS), the concept of quadri-partition neutrosophic soft locally compact space (QPNSLCS) is introduced in this research. It strengthens the theoretical foundation for handling uncertainty in complex topological structures by demonstrating that local compactness, particularly when combined with the Hausdorff requirement, entails the existence of compact neighbors and compactness in subspaces. The key concepts and theorems illustrate how compactness can be effectively used in the context of neutrosophic soft sets, which are a more powerful way to handle unclear and ambiguous data in advanced mathematical and practical applications. Furthermore, a number of machine learning algorithms are used to explore the concept of a tangent similarity between two quadri-partition neutrosophic soft sets. Additionally, the current study includes a number of studies and visualizations to evaluate the effectiveness of different clustering algorithms and dimensionality reduction techniques. Each of the graphics in the findings illustrates a distinct method for viewing and comprehending complex data. The K-means++ initialization (Fig. 6.1) serves as an illustration of how the algorithm's initialization step improves clustering accuracy by choosing centroid (data points) that are widely distributed, reducing the likelihood of subpar clustering performance. More training is required since hidden units are only activated with low activations, according to restricted Boltzmann Machine (RBM) activation patterns (Fig. 6.2). Additionally, the Linear Discriminant Analysis (LDA) plots (Fig. 6.4) and Heatmaps (Fig. 6.3) might provide helpful details regarding the organization and segregation of the datasets. The discussion of the results, which can be devoted to their applicability in terms of clustering, dimensionality reduction, and feature learning, is based on these methods and the associated visual models.

PT-Essential and PST-Essential Submodules

2025-12-03T02:19:29+08:00

Many generalizations have been presented in modules theory in order to present some new results in this direction. In this article, we introduced the concepts of PT-essential submodules and PST-essential submodules as a generalization to the concept of P-essential submodules. In particular, let ₳ be an R-module with Τ ≤ ₳. A submodule U of ₳ is called PT-essential in ₳ (U ≤_PTE ₳) in case there exist a submodule D of prime submodule P of ₳ in which U ≰ Τ, U ∩ D ≤ Τ implies D ≤ Τ. Furthermore, let ₳ be an R-module and Τ ≤ ₳. The submodule U of ₳ is said to be P-Small T-essential in ₳ (U ≤PST ₳) in condition that any small submodule D of prime submodule P of ₳ in which U ≰ Τ, U ∩ D ≤ Τ implies D ≤ Τ. Besides that, the concept of PT-complement submodule has been introduced with some properties about it. Finally, some basic properties of these concepts have been established. Then, several examples are given to illustrate the mentioned concepts.

Pythagorean Fuzzy \(\hat{Z}\)-Subalgebras in \(\hat{Z}\)-Algebraic Systems

2025-10-16T01:27:49+08:00

The idea of Pythagorean fuzzy sets was developed to improve the standard fuzzy set and intuitionistic fuzzy set theories by providing a more robust approach to handling uncertainty. This method provides greater flexibility in demonstrating membership, ensuring that the square sum of the degrees of membership and non-membership is maintained. This study examines how to incorporate Pythagorean fuzzy sets into the structure of the \(\hat{Z}\)-algebra, focusing on the properties of \(\hat{Z}\)-subalgebras. Pythagorean fuzzy \(\hat{Z}\)-subalgebras are a new notion that builds on traditional \(\hat{Z}\)-subalgebra structures. The purpose is to make algebra more creative when the conditions are uncertain. Significant developments in algebraic structures provide the theoretical basis for these fuzzy substructures. In addition, the Pythagorean fuzzy \(\hat{Z}\)-subalgebras under \(\hat{Z}\)-algebra homomorphism are examined, especially in relation to image and pre-image mappings.

Supermagic Triple Graphs

2025-11-18T23:35:14+08:00

A graph is called supermagic if it admits a labelling of edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we apply some effective methods to construct supermagic labellings of some triple graphs. Also, the application of supermagic graphs to balanced logistics network design in support of the United Nations Sustainable Development Goals is presented.

Political Connections and Bank Profitability: Evidence from Vietnamese Commercial Banks

2025-11-11T18:29:16+08:00

This study examines the impact of political connections, measured through state ownership and CEO political affiliation, on the profitability of Vietnamese Joint-Stock Commercial Banks from 2013 to 2023. The study employs OLS, FEM, REM, FGLS, and GMM models to address potential issues of endogeneity and heteroskedasticity. The results reveal that both SO and PC exert negative and statistically significant effects on bank profitability. In contrast, bank size and GDP growth have a positive influence on profitability, whereas non-performing loans and high liquidity ratios have a negative impact. This study presents novel empirical evidence of the effects of political connections on bank performance in Vietnam. It also offers policy insights suggesting that the State should reduce its ownership role, strengthen regulatory capacity, accelerate privatization, and promote independent and professional bank governance.

On Elliptic Equations with General Robin Boundary Conditions in Hölder Spaces: Non Commutative Cases

2025-10-31T06:29:55+08:00

In this paper, we study a class of second-order abstract differential equation problems of the elliptic type with operator coefficients with general Robin boundary conditions in a non-commutative setting, i.e the unbounded linear operator in the equation does not commute with the one that appears in the boundary conditions containing two spectral complex parameters. We study the case when the second member belongs to the Hölder space. We give necessary and sufficient conditions of compatibility to obtain a strict solution and also to ensure that the strict solution has the maximal regularity property. This paper is naturally the continuation of the ones studied in [16] and [10].

Digital Transformation and Competitive Advantage: A PLS-SEM Analysis of the Dual Mediation of Customer Participation and Innovation Capability

2025-11-27T02:22:36+08:00

This study pioneers an exploration of the mediating roles of customer participation (CP), service innovation capability (SIC), and process innovation capability (PIC) in the relationship between digital transformation (DT) and competitive advantage (CAD) among logistics enterprises, an aspect that has not been addressed in prior research. The research adopts a mixed-methods approach that integrates a systematic literature review, expert interviews, and a quantitative survey. Data were collected from 380 logistics enterprises operating in Ho Chi Minh City, Vietnam. Partial least squares structural equation modeling was employed to test the proposed relationships. The findings indicate that digital transformation (DT) has a positive effect on competitive advantage (CAD), customer participation (CP), service innovation capability (SIC), and process innovation capability (PIC). The study elucidates the mechanisms through which digital transformation (DT) influences competitive advantage (CAD). These findings provide important theoretical and practical implications, enabling firms to formulate more effective digital transformation strategies.

New Study on D−Paracompactness in Bitopological Spaces

2025-06-07T20:53:30+08:00

The new concept in the paper [1] of D-paracompact spaces is a well-studied type of topological space with rich structural properties and many applications in topological structures. That is, D-paracompact spaces are a natural extension of paracompact spaces in topology and provide a strong basis for understanding the relationship among local countableness, refinements, and D-covers. In this paper, we introduce the concept of pairwise D-paracompact spaces and their features relating to bitopological theory. Additionally, we will discuss the notion of D-paracompact spaces and describe a generalisation of bitopological space characteristics called pairwise D-paracompact spaces. This paper extends the theorems related to D-paracompact spaces in bitopological spaces and gives a number of theoretical findings, definitions, and properties that are thoroughly demonstrated.

Estimating the Norm of the Error Functional in Sobolev Space of Periodic Functions

2025-12-01T17:08:52+08:00

This article is devoted to obtaining an upper estimate of the error of an optimal quadrature formula for approximating the integral of periodic functions in the Sobolev space \(\widetilde{W_{2}^{(2,1,0)}}(0,1]\). In the quadrature formulas, a complex exponential weight function of the form \({{e}^{2\pi i\omega x}}\) is used. To minimize the norm of the error functional of the quadrature formula, a corresponding extremal function is found, and using it, an expression for the norm of the error functional is derived. The optimal coefficients that give the smallest value to this norm are obtained. Using Fourier analysis and the extremal function method, explicit formulas for the optimal coefficients are derived. These results extend the classical theory of quadrature formulas to the exponential-weight and oscillatory cases, providing efficient schemes for the numerical integration of periodic functions.

Siboid Topological Spaces

2025-08-20T17:26:18+08:00

In this article we introduce a new notion in topology that we call ‘siboid’, which yields to siboid topological spaces. We prove several fundamental results regarding siboid topological spaces. We define two new operators (.)^∗ and Φ and a new map cl^θ that satisfies the Kuratowski closure axioms whenever the siboid satisfies the property R. Moreover, various types of generalized open sets and generalized continuous functions are defined and studied, and ‘siboid’ is then connected with Boolean algebra.

A Finite Volume Method Solution to the Two-Assets Generalized Black-Scholes Equation

2025-11-30T05:11:24+08:00

The aim of this paper is to present a finite volume method (FVM) for solving numerically the two-assets generalized Black-Scholes equation. It it well-known that FVM is well-suited for solving problems involving hyperbolic and/or conservative laws mainly encountered in transport-diffusion and fluid dynamics problems. In this work, we attempt to use FVM for solving problems arising from market finance domain, in particular, the generalized multi-assets Black-Scholes problem. The discretization details and steps are presented for the two-assets problem. Then, numerical experiments are conducted on two main examples and show satisfactory results.

Analysis of Best Proximity Points in F-Metric Spaces with Applications

2025-11-10T06:53:15+08:00

The primary objective of this study is to introduce the concept of α-interpolative proximal contractions within the framework of F-metric spaces and to derive corresponding best proximity point results for these newly defined contractions. As a direct implication of the main theorems, best proximity results for single-valued mappings are also established. Moreover, we extend our investigation to partially ordered F-metric spaces, examining how graph structures influence best proximity point theory in this context. In addition, several fixed point theorems are obtained as immediate consequences of the proposed results. To illustrate the validity of our theoretical developments, non-trivial examples are provided.

Linear and Nonlinear Control for Complete Synchronization of Fractional-Order Discrete Reaction-Diffusion Systems

2025-07-20T17:12:33+08:00

This paper investigates complete synchronization (CS) of coupled fractional-order discrete reaction-diffusion systems (FO-RDs) under linear and nonlinear control strategies. We derive sufficient conditions for finite-time synchronization using Lyapunov functionals (LFs) and Caputo fractional difference operators. Theoretical results are validated through numerical simulations of the Degn-Harrison model, demonstrating that both control strategies achieve synchronization with zero error convergence. The linear controller shows faster convergence while the nonlinear controller exhibits superior robustness to initial condition variations.

On the Solvability of Quadratic Multi-Term Hybrid Equation with Nonlocal Hybrid Condition in Banach Algebra Spaces

2025-11-03T20:51:41+08:00

This paper investigates the existence of solutions for a class of multi-term hybrid functional equations subject to nonlocal and fractional conditions. We first establish sufficient conditions to ensure the existence of at least one continuous solution by applying Dhage’s fixed-point theorem within an appropriate Banach algebra framework. Subsequently, we extended the analysis to integrable solutions in the Lebesgue space L¹(J,R) under Carathéodory-type growth conditions. The uniqueness of solutions is then addressed by imposing Lipschitz-type constraints on nonlinear and hybrid terms. Furthermore, we examine the continuous dependence of solutions on initial data and parameters. Several illustrative examples are presented to demonstrate the applicability and validity of the obtained results. The theoretical framework developed here unifies and generalizes various existing results for hybrid and nonlocal fractional differential equations.

Estimation of Nucleation Parameters Using a Linear Optimal Control Problem

2025-08-11T19:32:23+08:00

In this paper, we consider a Becker-Doring-type mathematical interaction model between Aβ monomers and Aβ proto-oligomers, which play an important role in Alzheimer’s disease, with a given initial condition, but where the nucleation parameter is unknown. All of this work revolves around estimating the nucleation rate, which is not accessible experimentally. This estimation is made using techniques related to solving optimal control problems. We then propose a necessary and sufficient condition to ensure the existence and uniqueness of the solution, which should make it possible to estimate this parameter.

Variable Fractional-Order Reaction-Diffusion System for Edge Preservation in Biomedical Imaging

2025-12-01T00:17:23+08:00

This paper introduces a novel variable fractional-order reaction-diffusion system (VFO-RDs) to model anisotropic diffusion for edge preservation in biomedical imaging. By leveraging the Caputo nabla variable fractional-order difference operator, the proposed model captures the memory-dependent nature of biological tissues. We establish sufficient conditions for tempered Mittag-Leffler stability (MLS) of the equilibrium point using Lyapunov functions (LFs) and Lipschitz-type bounds on the nonlinear reaction term. Eigenvalue-based constraints on the discrete Laplacian guarantee contractive dynamics. Numerical simulations in both 1D and 2D domains demonstrate the edge-preserving capabilities of the method under various fractional-order (FO) scenarios. The results confirm that the proposed framework effectively maintains critical spatial features and improves stability, providing a viable tool for advanced biomedical image analysis.

Fixed Point Theorems for Contractive Mappings in Non–Archimedean Fuzzy Metric–Like Spaces

2025-11-08T05:26:54+08:00

A new fixed point theorem is established for generalized contractive mappings in NA-FMLS. The approach utilizes the ultrametric property of the fuzzy metric to ensure the convergence and uniqueness of the fixed point. This result extends several existing principles in fuzzy and b–metric settings and provides a unified framework for further applications in fuzzy nonlinear analysis.

New Categories of Generalized Fixed Point Theorems in New Generalization of Complete Metric Spaces with an Application

2025-11-13T04:59:01+08:00

The major objective of this manuscript is to present another novel extension of metric spaces namely; mapping weighted D-complete metric space. In the process, the uniqueness of various strictures of common and common coupled fixed point theorems have been investigated and verified for two pairs of self commutative maps under influence other improved types of extended contractive conditions in these spaces. On the other hand, a novel extended notion of Hausdorff distance namely; Hausdorff ∇^∗-distance has been defined in these spaces. Our second main results of various novel types of improved coincidence fixed point theorems have been obtained by applying the conception of generalized Hausdorff ∇^∗-distance. Additionally, various practical implementations of the existence fixed point for two pairs of self commutative maps as a solution for certain non-linear Volterra integral equations have been presented and investigated in the framework of map weighted D-complete metric spaces.

Localization Regimes for Quasilinear Parabolic p-Laplacian Equations under Unbounded Boundary Forcing

2025-10-31T10:15:56+08:00

This study formulates an open problem on spatial localization for quasilinear parabolic equations of pLaplacian type on the half-space R₊^N, with smooth, nonnegative initial data and boundary conditions that grow unbounded over time. While localization has been widely studied under homogeneous or decaying boundary conditions, its persistence under unbounded boundary input remains unresolved. We introduce two forms of spatial localization: effective localization, where the solution remains within a finite spatial domain, and strict localization, where it vanishes beyond a fixed boundary. The problem examines how the structure of the nonlinearities A(v) and B(v), and the growth rate of the boundary function ϕ influence solution confinement or spread. The study extends classical localization theory to degenerate and singular diffusion processes with diffusion exponent p > 1, offering new insight into spatial confinement under persistent external forcing.

Interval Valued Fuzzy Ordered Almost n-Interior-Ideals in Ordered Semigroups

2025-10-29T20:07:37+08:00

An almost ideal in a semigroup is a generalization of the concept of an ideal initiated by Grosek and Stako in 1980. In 2019, S. Suebsung et al. developed almost (m, n)-ideals in semigroups. Later, in 2021, T. Gaketem. introduced interval valued fuzzy almost (m, n)-ideals in semigroups. This paper aims we define interval valued fuzzy ordered almost n-interior ideals ordered semigroups. We prove some basic properties of interval valued fuzzy ordered almost n-interior ideals in ordered semigroups. And, we investigate a bridge between almost n-interior ideals and interval valued fuzzy ordered almost n-interior ideals in ordered semigroups.

Time Series Decomposition and LSTM Neural Networks for Forecasting Transportation CO2 Emissions in Saudi Arabia: Supporting Vision 2030 Climate Objectives

2025-08-06T15:02:32+08:00

This study develops an advanced forecasting framework by combining time series decomposition with Long Short-Term Memory (LSTM) neural networks to predict CO₂ emissions from Saudi Arabia’s transportation sector through 2034, in support of Vision 2030 climate objectives. Using historical data from 1970 to 2024, the results show that LSTM models significantly outperform traditional ARIMA approaches, achieving superior accuracy with an error rate of 6.82% for total emissions compared to 13.51% for ARIMA. The analysis focuses on CO₂ emissions in three sectors: road transport, aviation transport, and total transport emissions. Findings indicate that road transport is the dominant source, contributing over 95% of total emissions, with projections rising from 149.8 million tons in 2025 to 172.5 million tons by 2034. Aviation emissions are expected to increase from 3.79 to 6.61 million tons over the same period, while total transport emissions reflect the combined upward trend of both sectors. Despite a gradual decline in annual growth rates, the persistent increase in emissions underscores the urgent need for sustainable transport policies, particularly those that promote electric vehicles and expanded public transit systems. The study’s integration of STL decomposition with LSTM modeling provides a powerful, evidence-based tool for policymakers to guide CO2 mitigation strategies and track progress toward Vision 2030 climate targets.

Modeling Dual-Uncertainty In Sustainable Supplier Selection Using Bipolar Complex Pythagorean Fuzzy Sets

2025-12-01T04:55:14+08:00

Managing sustainability in modern supply chains requires decision-making tools that can accommodate conflicting criteria, uncertain data, and evaluations that involve both positive and negative impacts. To address these challenges, this study develops a new decision-making framework based on bipolar complex Pythagorean fuzzy sets (BCPFSs). The model integrates bipolarity, complex-valued membership degrees, and Pythagorean structures to capture the nuanced interplay of economic, environmental, and social considerations. On this foundation, two aggregation operators—the bipolar complex Pythagorean fuzzy weighted averaging (BCPFWA) and weighted geometric (BCPFWG) operators—are introduced to synthesize multidimensional information while preserving uncertainty and dual evaluations. The applicability of the framework is demonstrated through a case study on green supply chain management (GSCM). Six supplier strategies, ranging from cost-oriented to fully balanced sustainability-focused approaches, are assessed against eight attributes including cost efficiency, product quality, carbon emissions, waste management, technological integration, and social responsibility. The analysis reveals that the balanced sustainability supplier emerges as the most effective choice, consistently ranked highest by both operators. Comparative results with conventional fuzzy aggregation approaches show that the proposed operators provide richer, more stable, and more interpretable rankings, especially when trade-offs between cost and sustainability are present. This research contributes to both theory and practice: it extends the scope of fuzzy decision-making by unifying multiple existing models as special cases, and it offers a practical toolset for organizations seeking resilient and environmentally responsible supply chain solutions. The findings demonstrate that BCPF-based aggregation can enhance strategic decision-making in contexts where sustainability and uncertainty are inseparably linked.

Anti Synchronization of New Chaotic Systems via Adaptive Backstepping Control: An Application to Image Encryption

2025-11-03T06:36:04+08:00

Based on an adaptive backstepping control strategy, the anti-synchronization phenomenon between two identical chaotic systems is proposed to achieve global and exponential anti-synchronization. The theoretical analysis is supported by Lyapunov-based stability proofs. Through numerical simulations, it is demonstrate that the synchronization errors vanish asymptotically, thus confirming the validity of the proposed scheme. Furthermore, the practical applicability of the methodology is illustrated through its application instance to image encryption, where the master system states are employed in an XOR based process to encrypt visual data. The obtained results both the theoretical of the methodology and its applicability in secure communications and related fields.

Some Topological Properties in View of Hexa Topological Spaces

2025-11-08T20:54:15+08:00

In this paper, we introduced the definition of hexa topological space, also, we studied Some topological properties of this spaces with more illustrating examples. Many new definitions and theorems were investigated Separation axioms in hexa-topological spaces were debated, and many relations between these spaces and other topological spaces were discussed.

Extended Bipolar Intuitionistic Fuzzy Ideals Framework Through Level Sets and Its Characterization via Regular Ordered Γ-Semigroups

2025-06-23T00:24:02+08:00

This paper proposes an extended framework for bipolar anti-intuitionistic fuzzy ideals within the context of ordered Γ-semigroups. We introduce and investigate the (δ, τ)-bipolar anti-intuitionistic fuzzy subsemigroups (BPAIFSS), including their associated left ideals, right ideals, ideals, and bi-ideals. These structures generalize existing fuzzy ideal notions by incorporating dual-valued membership and non-membership functions with flexible threshold control. Using level set analysis, we characterize the algebraic properties of these fuzzy ideals and establish their role in determining the regularity of ordered Γ-semigroups. Illustrative examples are provided to validate and demonstrate the applicability of the theoretical results.

Iterative Methods for General Bivariational Inequalities

2025-10-09T13:01:20+08:00

Some new classes of general bivariational inequalities, which can be viewed as a novel important special case of variational equalities, are investigated. Projection method, auxiliary principle and dynamical systems coupled with finite difference approach are used to suggest and analyzed a number of new and known numerical techniques for solving bivariational inequalities. Convergence analysis of these methods is investigated under suitable conditions. One can obtain a number of new classes of bivariational inequalities by interchanging the role of operators. Sensitivi anaysis of the bivariational inequalities is also discussed. Some important special cases are highlighted. Several open problems are suggested for future research.

Codimension Two Bifurcation Analysis of a Discrete Coupled Competition Duopoly Game

2025-11-12T04:10:00+08:00

This paper analytically examines the coupled competition duopoly game model. This study examines the codimension-two bifurcations of different types of the model through bifurcation theory and numerical continuation methods. The model undergoes codimension-two bifurcation, heteroclinic bifurcation near the 1:2 point, a homoclinic structure near the 1:3 resonance point, and an invariant cycle bifurcated by a period 4 orbit near the 1:4 resonance point. Subsequently, numerical simulations are performed to validate the theoretical study.

A Novel Approach to D-Stability and Additive D-Stability of Economic Models

2025-09-10T16:18:39+08:00

The study of \(D\)-stability in mathematical analysis is crucial for understanding and ensuring the stability of linear dynamical systems. This article introduces novel findings on the characterization of \(D\)-stability, along with its connections to additive \(D\)-stability concerning speed and coordinate transformations in linear dynamical systems with \(n\) degrees of freedom
\[
A \frac{d^2\mu(\tau)}{d\tau^2} + B \frac{d\mu(\tau)}{d\tau} + C \mu(\tau) = 0, \ \tau \in \mathbb{R}, \ \tau > 0,
\]
Consider the stiffness, mass, and damping matrices \(A, B, C \in \mathcal{M}^{n \times n}\), and let \( \mu(\tau) \in \mathbb{R}^n \) denote the vector of generalized coordinates with \(\frac{d\mu(\tau)}{d\tau}\) representing its corresponding velocity vector. This work derives new theoretical insights into \(D\)-stability, additive \(D\)-stability with respect to velocity, and additive \(D\)-stability concerning coordinate transformations. These results are established using techniques from linear algebra, matrix theory, dynamical systems, and their connections to structured singular value computations. Additionally, numerical investigations of the spectrum, singular values, and pseudospectra of the coefficient matrices \(A, B, C \in \mathcal{M}^{n \times n}\) are conducted using EigTool, providing further validation of the theoretical framework.

On the Analysis and Solution Structure of Generalized Hemivariational Inclusion Problems

2025-04-23T10:39:46+08:00

This paper introduces and analyzes a new class of generalized hemivariational inclusion problems. We establish the existence and uniqueness of solutions under mild assumptions and develop an efficient iterative algorithm for their numerical approximation. To demonstrate the practical utility of our theoretical framework, we apply it to a frictional contact problem in elasticity. The model involves an elastic body in contact with a rigid foundation, governed by a nonmonotone friction law that depends on both normal and tangential displacements. Our results provide a comprehensive solution, from theory to computation, for this challenging class of nonsmooth systems.

Spherical Curves and Their Rigidity in Metric Spaces with Lower Curvature Bounds

2025-11-20T10:55:26+08:00

In this paper, we examine geometric relationships between metric spaces with curvature bounded below and their corresponding model spaces of constant curvature. Let \(\gamma\) be a closed spherical curve in a metric space whose curvature is bounded below by \(K\), lying at a distance \(r < \tfrac{\pi}{2\sqrt{K}}\) from a point. Let \(\gamma^{\prime}\) denote the circle of radius \(r\) centered at the corresponding point in the model space of constant curvature \(K\). Under suitable geometric equivalence conditions—namely, the preservation of pairwise distances between corresponding points of \(\gamma\) and \(\gamma^{\prime}\), the isometry of convex hulls of corresponding geodesic triangles, and the equality of arc lengths or total curvature—we show that the geodesic surface enclosed by \(\gamma\) is isometric to the region bounded by \(\gamma^{\prime}\). This result offers a foundational geometric characterization of metric spaces with curvature bounded below through their model counterparts and provides a framework for further study of total curvature, convexity, and isometric embeddings in such spaces.

Analytical Study for Stagnation-Point Flow and Heat Transfer of MHD Nanofluid Over a Stretching Sheet in Porous Medium via Modified Adomian Decomposition Method

2025-10-22T01:33:02+08:00

In the current study, we investigate the stagnation-point flow of a MHD nanofluid toward stretching sheet in porous media with suction or injection. Whereas, the contribution of the velocity, temperature, and nanoparticle distributions to identify the advantages or disadvantages that nanoparticles like bacteria, microbes and viruses, cause in the flow stretching sheet is what makes this work significan. A new procedure is suggested for the analytical treatment of the governing system of partial differential equations, where the boundary condition at infinity is converted from the unbounded domain to the bounded domain by using some transformations and then modified adomian decomposition method is utilized. The effects of parameters (porous medium, magnetic number, surface heat flux, suction or injection and Prandtl number) on velocity, temperature and concentration profiles are shown graphically and analyzed. Finally, we compared our obtained results with the other techniques used before in literature.

Neutrosophic Semi δ-pre Irresolute Mappings

2025-07-02T06:45:53+08:00

This study investigates and defined new concept of irresolute mappings called Neutrosophic semi δ-pre irresolute mappings via Neutrosophic topological spaces. Several preservation properties and some characterizations concerning Neutrosophic semi δ-pre irresolute have been obtained.

On Semi α-Lindelöf in Bitopological Spaces

2025-11-13T04:28:55+08:00

This paper set up a Closure–operator scheme for semi–\(\alpha\)–Lindel\"{o}fness in bitopological spaces to manage covering behavior generated by two interacting topologies. With the Čech–closure hull \(H_{ij}=j\!\operatorname{cl}\,i\!\operatorname{int}\,j\!\operatorname{cl}\,i\!\operatorname{int}\), we reformulate \(ij\)–semi–\(\alpha\)–open sets and obtain operator–level criteria for \(ij\)–semi–\(\alpha\)–Lindel\"{o}fness. We prove a network estimate that bounds \(L^{S_\alpha}_{ij}\) by the size of an \(ij\)–\(S_\alpha\)–network, and a star criterion under \(\rho\)–discrete network decompositions of such networks. Structural consequences include hereditary and transfer over dense subsets, stability under countable sums, and a tube–type product when the second topology is discrete and the first factor is \(i\)–compact. Also, we introduce \(ij\)–\(S_\alpha\)–perfect mappings and show preservation of \(ij\)–\(S_\alpha\)–Lindelöfness with explicit cardinal bounds; images under \(ij\)–\(S_\alpha\)– and \(ij\)–\(S_\alpha^\ast\)–continuous maps are correspondingly controlled. Pairwise invariants are examined via \(\widehat L^{S_\alpha}_{\mathrm{pair}}\), which lies between the one–sided quantities and equals their maximum whenever at least one is infinite.

Enhancing Water Level Forecasting Performance in High-Variability Basins through Data Restructuring: A Case Study of the Yom River Basin, Thailand

2025-06-26T22:34:46+08:00

The Yom river basin in one of the 22 main river basins of Thailand. This experiences perennial floods and droughts that heavily impact the agricultural sector. In order to reduce the impact, water management, including water level estimation. A considerable task of management is the quantitative forecasting of water levels. This study proposes appropriate forecasting models for time series of daily water level data from four water level measurement stations. The study period is from 2007 to 2022 on September. The efficiency of this forecasting model was determined from comparisons to three approaches, centered moving average model (CMA), additive decomposition model (DEC), Holt’s Winter additive model (WIN). Results indicated that: The forecasts of two years gave similar forecast patterns to the previously observed values. Mainly, (decomposition) was more accurate than the other approaches for all stations. The RMSEs of upstream was slightly greater than the downstream RMSEs for three approaches.

Analyzing Extreme Water Volume Events in Khwae Noi Bamrung Daen Dam: A Statistical Approach

2025-11-08T09:45:25+08:00

This study focuses on the statistical modeling of extreme water volumes at the Kwae Noi Bamrung Daen Dam in Phitsanulok Province using extreme value theory (EVT). The objective is to predict high water levels that may pose risks to dam safety and operations. Historical monthly water volume data from 2011 to 2023 were analyzed using the generalized extreme value (GEV) distribution. The Jarque-Bera test confirmed a non-normal distribution (p = 0.02906), justifying the use of EVT. Maximum likelihood estimation yielded parameter estimates of µ = 446.58, σ = 228.68, and ξ = -0.13. Goodness-of-fit tests (K-S and A-D) confirmed the adequacy of the GEV model, with p-values of 0.3559 and 0.1124, respectively. The model estimated that extreme water volumes exceeding 950 million cubic meters are expected approximately once every 25 years. These findings contribute to more accurate hydrological forecasting, improved early warning systems, and enhanced water resource management policies. The study supports risk-informed decision-making in flood-prone regions and advances the application of EVT in dam safety and environmental planning.

Essential Norm of Composition Operators on Harmonic Zygmund Spaces and Their Derivative Spaces

2025-09-17T16:04:04+08:00

Let ψ represent the analytic self-mapping within the unit disk D. We define the composition operator C_ψ as C_ψf = f◦ψ for every f belonging to the space of harmonic functions H(D). The essential norm of composition operators within specific harmonic mapping spaces is investigated in this research. Explicitly, we outline the essential norm of composition operators on the harmonic Zygmund spaces Z^H and the derivative of harmonic Zygmund spaces V^H. Notably, these results extend and build upon results that were established previously for the analytic settings.

Fractal-Fractional Modeling and Analysis of Monkeypox Disease Using Atangana-Baleanu Derivative

2025-04-10T22:15:19+08:00

In this study, we formulate a deterministic mathematical model to describe the transmission dynamics of the monkeypox virus using fractal and fractional-order differential equations. The model incorporates all possible interactions influencing disease propagation within the population. Our analysis primarily focuses on the stability of fractal–fractional derivatives, aiming to establish the existence and uniqueness of solutions through the fixed-point theorem. Additionally, we examine Ulam-Hyers stability and other significant findings related to the proposed model. To enhance numerical accuracy, we employ Lagrange polynomial interpolation for computational approximations. Finally, graphical simulations for various fractal–fractional orders are presented to validate the model’s effectiveness and demonstrate its practical relevance.

Analytic Estimates for Bi-Univalent Functions Associated with a New Operator Involving the q–Rabotnov Function

2025-10-05T05:14:57+08:00

In this paper, we introduce and analyze a new subclass of bi-univalent functions associated with a differential operator constructed from the q–Rabotnov function. Motivated by the framework of q–calculus and its interplay with geometric function theory, the proposed operator is defined through convolution with q–Rabotnov kernels, thereby generating novel analytic structures. By applying the subordination principle, we establish sharp coefficient estimates for the initial Taylor–Maclaurin coefficients |α₂| and |α₃|, and derive Fekete–Szegö type inequalities for the class under consideration. The results presented here extend and generalize several recent contributions in the theory of biunivalent functions, highlighting the central role of q–special functions in the development of new operator-based subclasses. These findings provide deeper insights into the analytic behavior of bi-univalent mappings and suggest further applications of q–calculus in operator theory, convolution structures, and complex analysis.