A Class of p-Valent Close-to-Convex Functions Defined Using Gegenbauer Polynomials

Authors

DOI:

https://doi.org/10.37256/cm.5420245414

Keywords:

analytic functions, holomorphic functions, univalent functions, <i>p</i>-valent functions, principle of subordination, gegenbauer polynomials, chebyshev polynomials, coefficient estimates, fekete-szegö inequality

Abstract

A new class of p-valent close-to-convex functions is introduced in this paper, which is defined using Gegenbauer Polynomials within the open unit disk D. This investigation sheds light on the properties and behaviors of these p-valent close-to-convex functions, providing estimations for the modulus of the coefficients ap+1 and ap+2, with p being a natural number, for functions falling under this particular class. Additionally, this paper also investigates the classical Fekete-Szegö functional problem for functions f that are part of the aforementioned class.

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Published

2024-12-12

Issue

Contemporary Mathematics, Volume 5 Issue 4 (2024), 4132-6581

Section

Research Article

License

Copyright (c) 2024 Waleed Al-Rawashdeh.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
A Class of p-Valent Close-to-Convex Functions Defined Using Gegenbauer Polynomials. Contemp. Math. [Internet]. 2024 Dec. 12 [cited 2025 Dec. 24];5(4):6093-102. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/5414