Fekete-Szegö Functional of a Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials

Authors

  • Waleed AlRawashdeh Zarqa University

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i1.5004

Keywords:

Analytic Functions; Taylor-Maclaurin Series; Univalent and Bi-Univalent Functions; Principle of Subordination; Hadamard Product; Ruscheweyh Operator; Ruscheweyh Derivative; Gegenbauer Polynomials; Chebyshev polynomials; Coefficient estimates; Fekete-Szeg\

Abstract

In this paper, we introduce and investigate a class of bi-univalent functions, denoted by $\mathcal{F}(n, \alpha, \beta)$, that depends on the Ruscheweyh operator. For functions in this class, we derive the estimations for the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. Moreover, we obtain the classical Fekete-Szeg\"{o} inequality of functions belonging to this class.

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Published

2024-01-31

Issue

Section

Nonlinear Analysis

How to Cite

Fekete-Szegö Functional of a Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials. (2024). European Journal of Pure and Applied Mathematics, 17(1), 105-115. https://doi.org/10.29020/nybg.ejpam.v17i1.5004