Coefficient Bounds for Certain Classes of Analytic Functions of Complex Order γ Associated with Cardioid Domain
DOI:
https://doi.org/10.53560/PPASA(62-2)860Keywords:
Analytic Functions, Starlike and Convex Functions, Subordination, Cardioid Domain, Coefficient Bounds, Fekete-Szegö ProblemAbstract
In this paper, new Ma–Minda type subclasses of analytic functions of complex order γ, associated with cardioid domain in the open unit disk , are introduced. The objective of this work is to investigate the first three sharp coefficient bounds and to examine the sharp estimates of the Fekete-Szegö problem for these subclasses.
References
1. C. Tom (Ed.). Univalent Functions: The Basics (Chapter 8). In: Geometric Function Theory. Springer, Cham, Switzerland pp. 203-225 (2024).
2. A.W. Goodman (Ed.). Univalent functions. Vol. I. Mariner Publishing Company (1983).
3. A.W. Goodman (Ed.). Univalent functions. Vol. II. Mariner Publishing Company (1983).
4. C. Pommerenke (Ed.). Univalent Functions. Vandenhoeck and Ruprecht, Göttingen (1975).
5. D.K. Thomas, N. Tuneski, and A. Vasudevarao (Eds.). Univalent functions. Part of: De Gruyter Studies in Mathematics. De Gruyter, Berlin (2018).
6. P.L. Duren (Ed.). Univalent functions. Part of the book series: Grundlehren der mathematischen Wissenschaften (Volume 259). Springer-Verlag, New York (1983).
7. N.E. Cho, V. Kumar, and V. Ravichandran. A survey on coefficient estimates for Caratheodory functions. Applied Mathematics E-Notes 19: 370-396 (2019).
8. V. Kumar, N.E. Cho, V. Ravichandran, and H.M. Srivastava. Sharp coefficient bounds for starlike functions associated with the Bell numbers. Mathematica Slovaca 69(5): 1053-1064 (2019).
9. Y.J. Sun, M. Arif, L. Shi, and M.I. Faisal. Some further coefficient bounds on a new subclass of analytic functions. Mathematics 11(12): 2784 (2023).
10. M. Fekete and G. Szegö. Eine Bemerkung uber ungerade schlichte Funktionen. Journal of the London Mathematical Society 8: 85-89 (1933).
11. S. Kanas and H.E. Darwish. Fekete-Szegö problem for starlike and convex functions of complex order. Applied Mathematics Letters 23: 777-782 (2010).
12. Ahmed, A.W. Shaikh, and S.A. Shah. Fekete-Szegö Problem for Certain Analytic Functions of Complex Order Associated with Cardioid Domain. International Journal of Analysis and Applications 23: 109-109 (2025).
13. W. Ma and D. Minda. A unified treatment of some special classes of functions. In: Proceedings of the Conference on Complex Analysis. Nankai Institute of Mathematics, Nankai University, Tianjin, China pp. 157-169 (1992).
14. W. Janowski, Some extremal problems for certain families of analytic functions I. In Annales Polonici Mathematici 28(3): 297-326 (1973).
15. M.S. Robertson. On the theory of univalent functions. Annals of Mathematics 37(2): 374-408 (1936).
16. N.E. Cho, V. Kumar, S.S. Kumar, and V. Ravichandran. Radius problems for starlike functions associated with the sine function. Bulletin of the Iranian Mathematical Society 45: 213-232 (2019).
17. M.K. Aouf, J. Dziok, and J. Sokol. On a subclass of strongly starlike functions. Applied Mathematics Letters 24(1): 27-32 (2011).
18. J. Sokoł and J. Stankiewicz. Radius of convexity of some subclasses of strongly starlike functions. Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka 19: 101-105 (1996).
19. S.S. Kumar and G. Kamaljeet. A cardioid domain and starlike functions. Analysis and Mathematical Physics 11(2): 34 (2021).
20. K. Sharma, N.K. Jain, and V. Ravichandran. Starlike functions associated with a cardioid. Afrika Matematika 27: 923-939 (2016).
21. V. Ravichandran, P. Yasar, B. Metin, and S. Arzu. Certain subclasses of starlike and convex functions of complex order. Hacettepe Journal of Mathematics and Statistics 34: 9-15 (2005).
22. S.B. Al-Shaikh, K. Matarneh, A.A. Abubaker, and M.F. Khan. Sharp Coefficient Bounds for a New Subclass of Starlike Functions of Complex Order γ Associated with Cardioid Domain. Mathematics 11(9): 2017 (2023).
23. S. Kanas and F. Ronning. Uniformly starlike and convex functions and other related classes of univalent functions. Annales Universitatis Mariae Curie-Skłodowska. Sectio A 53: 95-105 (1999).
24. F.R. Keogh and E.P. Merkes. A coefficient inequality for certain classes of analytic functions. Proceedings of the American Mathematical Society 20: 8-12 (1969).

