SavedAdd your journal

Journals / Eastern Anatolian Journal of Science / 2025 / Volume: 11 Issue: 1-2

Coefficient Bound Estimates and Fekete-Szegö Problem for the Certain Analytic and Univalent Function Classes Subordinated to the Improved q-Exponential Function

Nizami Mustafa(KAFKAS UNIVERSITY)0000-0002-2758-0274
Veysel Nezir(KAFKAS UNIVERSITY)
Pages
—
Publication Date
2025-12-29
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Here, we give some coefficient upper bound estimates and solve Fekete-Szegö problem for this definition class.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we define a new subclass of convex univalent functions defined in the open unit disk of the complex plane, subordinated to the improved exponential function.
📊
Key Findings & Data:In this study, we define a new subclass of convex univalent functions defined in the open unit disk of the complex plane, subordinated to the improved exponential function.
💡
Conclusion & Impact:Here, we give some coefficient upper bound estimates and solve Fekete-Szegö problem for this definition class.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Analytic function · convex function · univalent function

Abstract

In this study, we define a new subclass of convex univalent functions defined in the open unit disk of the complex plane, subordinated to the improved exponential function. Here, we give some coefficient upper bound estimates and solve Fekete-Szegö problem for this definition class.

🔖

Cite This Article

Mustafa, N., Nezir, V. (2025). Coefficient Bound Estimates and Fekete-Szegö Problem for the Certain Analytic and Univalent Function Classes Subordinated to the Improved q-Exponential Function. Eastern Anatolian Journal of Science, Volume: 11 Issue: 1-2. https://ajindex.com/articles/1475621

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (27)

  1. ALOTAIBI, A., ARIF, M., ALGHAMDI, M. A., HUSSAIN, S. (2020). Starlikeness associated with cosine hyperbolic function. Mathematics, 8, 1118.
  2. ALSOBOH, A., ÇAĞLAR, M., BUYANKARA, M. (2022). Fekete–Szegö inequality for a subclass of bi-univalent functions linked to q-ultraspherical polynomials. Contemporary Mathematics, 5(2), 2366–2380.
  3. ARIF, M., AHMAD, K., LIU, J.-L., SOKOL, J. (2019). A new class of analytic functions associated with Salagean operator. J. Funct. Spaces, Article ID 5157394.
  4. BANO, K., RAZA, M. (2020). Starlike functions associated with cosine function. Bull. Iran. Math. Soc., 47, 1513–1532.
  5. BIEBERBACH, L. (1916). Über die Koeffizienten derjenigen Potenzreihen welche eine schlichte Abbildung des Einheitskreises vermitteln. Sitzungsberichte Preuss. Akad. Wiss., 940–955.
  6. BRANNAN, D. A., KIRWAN, W. E. (1969). On some classes of bounded univalent functions. J. Lond. Math. Soc., 2, 431–443.
  7. CIESLINSKI, J. L. (2011). Improved exponential and trigonometric functions. Applied Mathematics Letters, 24(12), 2110–2114.
  8. ÇAĞLAR, M., BUYANKARA, M., KARAMAN, A. (2024). Fekete–Szegö inequalities for Sakaguchi type bi-univalent functions defined by Gegenbauer polynomials. Turkish Journal of Science, 9(2), 126–136.
  9. ÇAĞLAR, M., ORHAN, H., SRIVASTAVA, H. M. (2020). Coefficient bounds for q-starlike functions associated with q-Bernoulli numbers. Journal of Applied Analysis and Computation, 15(4), 2354–2364.
  10. DUREN, P. L. (1983). Univalent Functions. Grundlehren der Mathematischen Wissenschaften, Vol. 259. Springer-Verlag, New York.
  11. KOEBE, P. (1909). Über die Uniformisierung der algebraischen Kurven, durch automorphe Funktionen mit imaginärer Substitutionsgruppe. Nachr. Akad. Wiss. Göttingen Math.-Phys., 68–76.
  12. KUMAR, S. S., ARORA, K. (2020). Starlike functions associated with a petal shaped domain. arXiv preprint arXiv:2010.10072.
  13. MENDIRATTA, R., NAGPAL, S., RAVICHRANDRAN, V. (2015). On a subclass of strongly starlike functions associated with exponential function. Bull. Malays. Math. Soc., 38, 365–386.
  14. MILLER, S. S. (1975). Differential inequalities and Carathéodory functions. Bull. Amer. Math. Soc., 81, 79–81.
  15. MUSTAFA, N., NEZIR, V., KANKILIÇ, A. (2023a). Coefficient estimates for certain subclass of analytic and univalent functions associated with sine hyperbolic function. 13th Int. İstanbul Scientific Research Congress, April 29–30, 234–241, İstanbul, Turkey.
  16. MUSTAFA, N., NEZIR, V., KANKILIÇ, A. (2023b). The Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine hyperbolic function. 13th Int. İstanbul Scientific Research Congress, April 29–30, 242–249, İstanbul, Turkey.
  17. MUSTAFA, N., NEZIR, V. (2023c). Coefficient estimates and Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine hyperbolic function. 13th Int. İstanbul Scientific Research Congress, May 1–2, 475–481, İstanbul, Turkey.
  18. MUSTAFA, N., NEZIR, V. (2024). Coefficient estimates and Fekete–Szegö problem for certain subclass of analytic and univalent functions associated with sine hyperbolic function of complex order. Turkish Journal of Science, 9(1), 45–53.
  19. MUSTAFA, N., DEMIR, H. A. (2023d). Coefficient estimates for certain subclass of analytic and univalent functions associated with sine and cosine functions. 4th Int. Black Sea Congress on Modern Scientific Research, June 6–8, 2555–2563, Rize, Turkey.
  20. MUSTAFA, N., DEMIR, H. A. (2023e). Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine and cosine functions. 4th Int. Black Sea Congress on Modern Scientific Research, June 6–8, 2564–2572, Rize, Turkey.
  21. MUSTAFA, N., NEZIR, V., KANKILIÇ, A. (2023f). Coefficient estimates for certain subclass of analytic and univalent functions associated with sine hyperbolic function with complex order. Journal of Scientific and Engineering Research, 10(6), 18–25.
  22. MUSTAFA, N., NEZIR, V., KANKILIÇ, A. (2023g). The Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine hyperbolic function with complex order. Eastern Anatolian Journal of Science, 9(1), 1–6.
  23. MUSTAFA, N., DEMIR, H. A. (2023h). Coefficient estimates for certain subclass of analytic and univalent functions associated with sine and cosine functions with complex order. Journal of Scientific and Engineering Research, 10(6), 131–140.
  24. SHARMA, K., JAIN, N. K., RAVICHRANDRAN, V. (2016). Starlike function associated with a cardioid. Afr. Math., 27, 923–939.
  25. SOKOL, J. (2011). A certain class of starlike functions. Comput. Math. Appl., 62, 611–619.
  26. SOKOL, J., STANKIEWICZ, J. (1996). Radius of convexity of some subclasses of strongly starlike functions. Zesz. Nauk. Politech. Rzesz. Math., 19, 101–105.
  27. ULLAH, K., ZAINAB, S., ARIF, M., DARUS, M., SHUTAYI, M. (2021). Radius problems for starlike functions associated with the tan hyperbolic function. J. Funct. Spaces, Article ID 9967640.