Applications of Neutrosophic in Third-Order Differential Subordinations of Multivalent Functions

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-24-2026-314
Published: Oct 5, 2026
Cite as:
Suha Hammad, Ala Amourah, Mohammad El-Ityan, Abdullah Alsoboh, Mohammed M. Al-Hatmi, Fadi M.A. Al-Zu’bi, Tariq Al-Hawary, Applications of Neutrosophic in Third-Order Differential Subordinations of Multivalent Functions, Int. J. Anal. Appl., 24 (2026), 314.

Main Article Content

Suha Hammad, Ala Amourah, Mohammad El-Ityan, Abdullah Alsoboh, Mohammed M. Al-Hatmi, Fadi M.A. Al-Zu’bi, Tariq Al-Hawary

Abstract

In this work, we investigate third-order differential subordination for multivalent functions using the Cho-Kwon-Srivastava operator with the neutrosophic parameter \(\mathcal{M}_\aleph\). By incorporating uncertainty, our approach extends classical models and provides a flexible framework to analyze the behavior of multivalent functions under both precise and uncertain settings. These results generalize previous studies, offering deeper insights into the structure and properties of such functions.

Article Details

References

  1. A.T. Oladipo, Bounds for Poisson and Neutrosophic Poisson Distributions Associated with Chebyshev Polynomials, Palestine J. Math. 10 (2021), 169–174. https://zbmath.org/7335998.
  2. J.A. Antonino, S.S. Miller, Third-Order Differential Inequalities and Subordinations in the Complex Plane, Complex Var. Elliptic Equ. 56 (2011), 439–454. https://doi.org/10.1080/17476931003728404.
  3. F. Smarandache, J. Dezert, S. Bhattacharya, A. Buller, M. Khoshnevisan, et al., Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics, arXiv:math/0306384, 2003. https://doi.org/10.48550/arXiv.math/0306384.
  4. F. Smarandache, Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability, Sitech, (2013). https://doi.org/10.48550/arXiv.1311.7139.
  5. K.F. Alhasan, A.A. Salama, Introduction to Neutrosophic Reliability Theory, Int. J. Neutrosophic Sci. 15 (2021), 52–61. https://doi.org/10.5281/zenodo.5033829.
  6. F. Smarandache, Neutropsychic Personality: A Mathematical Approach to Psychology, Pons, (2018). https://digitalrepository.unm.edu/math_fsp/29/.
  7. I.M. Hanafy, A.A. Salama, K.M. Mahfouz, Correlation Coefficients of Neutrosophic Sets by Centroid Method, Int. J. Probab. Stat. 2 (2013), 9–12.
  8. I.M. Hanafy, A.A. Salama, K. Mahfouz, Correlation of Neutrosophic Data, Int. Ref. J. Eng. Sci. 1 (2012), 39–43.
  9. H. ElWahsh, M. Gamal, A.A. Salama, I.M. El-Henawy, Intrusion Detection System and Neutrosophic Theory for MANETs: a Comparative Study, Neutrosophic Sets Syst. 23 (2018), 16–22. https://doi.org/10.5281/zenodo.2155075.
  10. H. Elwahsh, M. Gamal, A.A. Salama, I.M. El-Henawy, Modeling Neutrosophic Data by Self-Organizing Feature Map: MANETs Data Case Study, Procedia Comput. Sci. 121 (2017), 152–159. https://doi.org/10.1016/j.procs.2017.11.021.
  11. A. Salama, H.A. El-Ghareeb, A.M. Manie, F. Smarandache, Introduction to Develop Some Software Programs for Dealing with Neutrosophic Sets, Neutrosophic Sets Syst. 3 (2014), 51–52.
  12. A.B. AL-Nafee, F. Smarandache, A.A. Salama, New Types of Neutrosophic Crisp Closed Sets, Neutrosoph. Sets Syst. 36 (2020), 175–183. https://doi.org/10.5281/zenodo.4065428.
  13. A.A. Salama, M. Eisa, H. ElGhawalby, A.E. Fawzy, A New Approach in Content-Based Image Retrieval Neutrosophic Domain, in: C. Kahraman, İ. Otay (eds.), Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets, Studies in Fuzziness and Soft Computing, Springer, Cham, pp. 361–369, (2019). https://doi.org/10.1007/978-3-030-00045-5_14.
  14. F.M. Mohammed, S.F. Matar, Fuzzy Neutrosophic Alpha-m-Closed Sets in Fuzzy Neutrosophic Topological Spaces, Neutrosophic Sets Syst. 21 (2018), 56–65. https://fs.unm.edu/NSS/FuzzyNeutrosophicAlphaM.pdf.
  15. N.E. Cho, O.S. Kwon, H.M. Srivastava, Inclusion Relationships and Argument Properties for Certain Subclasses of Multivalent Functions Associated with a Family of Linear Operators, J. Math. Anal. Appl. 292 (2004), 470–483. https://doi.org/10.1016/j.jmaa.2003.12.026.
  16. A. Çetinkaya, L.-I. Cotîrlă, Briot–Bouquet Differential Subordinations for Analytic Functions Involving the Struve Function, Fractal Fract. 6 (2022), 540. https://doi.org/10.3390/fractalfract6100540.
  17. H.A. Farzana, M.P. Jeyaraman, T. Bulboacă, On Certain Subordination Properties of a Linear Operator, J. Fract. Calc. Appl. 12 (2021), 148–162.
  18. S. Porwal, G. Murugusundaramoorthy, Geometric Properties of a New Integral Operator Associated with Dini Functions, Electron. J. Math. Anal. Appl. 10 (2022), 267–274. https://doi.org/10.21608/ejmaa.2022.292057.
  19. T.M. Seoudy, Second Order Differential Subordination and Superordination of Liu-Srivastava Operator on Meromorphic Functions, Afr. Mat. 32 (2021), 1399–1408. https://doi.org/10.1007/s13370-021-00907-4.
  20. H.M. Srivastava, A. Prajapati, P. Gochhayat, Third-Order Differential Subordination and Differential Superordination Results for Analytic Functions Involving the Srivastava-Attiya Operator, Appl. Math. Inf. Sci. 12 (2018), 469–481. https://doi.org/10.18576/amis/120301.
  21. A. Almalkawi, A. Alsoboh, A. Amourah, T. Sasa, Estimates for the Coefficients of Subclasses Defined by the q-Babalola Convolution Operator of Bi-Univalent Functions Subordinate to the q-Fibonacci Analogue, Eur. J. Pure Appl. Math. 18 (2025), 6499. https://doi.org/10.29020/nybg.ejpam.v18i3.6499.
  22. M. Ahmed, A. Alsoboh, A. Amourah, J. Salah, On the Fractional q-Differintegral Operator for Subclasses of Bi-Univalent Functions Subordinate to q-Ultraspherical Polynomials, Eur. J. Pure Appl. Math. 18 (2025), 6586. https://doi.org/10.29020/nybg.ejpam.v18i3.6586.
  23. A. Alsoboh, M. Çağlar, M. Buyankara, Fekete–Szegö Inequality for a Subclass of Bi-Univalent Functions Linked to q-Ultraspherical Polynomials, Contemp. Math. 5 (2024), 2531–2545. https://doi.org/10.37256/cm.5220243737.
  24. A. Alsoboh, A. Amourah, W.G. Atshan, J. Salah, T. Sasa, A Study of Bi-Univalent Class in Leaf-Like Domains Using Quantum Calculus Through Subordination, Int. J. Anal. Appl. 23 (2025), 293. https://doi.org/10.28924/2291-8639-23-2025-293.
  25. A. Alsoboh, A. Amourah, A. Al Kasbi, J. Salah, A.A.-R. Malkawi, T. Sasa, A Novel Subclass of Bi-Univalent Functions Defined by the q-Wright Operator and the q-Analogue of Fibonacci Numbers, Int. J. Anal. Appl. 24 (2026), 78. https://doi.org/10.28924/2291-8639-24-2026-78.
  26. A.S. Tayyah, W.G. Atshan, Differential Subordination and Superordination Results for p-Valent Analytic Functions Associated with (r,k)-Srivastava Fractional Integral Calculus, MethodsX 13 (2024), 103079. https://doi.org/10.1016/j.mex.2024.103079.
  27. A.S. Tayyah, W.G. Atshan, G.I. Oros, Third-Order Differential Subordination Results for Meromorphic Functions Associated with the Inverse of the Legendre Chi Function via the Mittag-Leffler Identity, Mathematics 13 (2025), 2089. https://doi.org/10.3390/math13132089.