International Journal of Analysis and Applications

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

Munirah Aljuaid — Tue, 06 Jan 2026 00:00:00 +0800

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

Tue, 06 Jan 2026 00:00:00 +0800

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

Tue, 06 Jan 2026 00:00:00 +0800

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.