Fekete-Szegö Functional of a Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i1.5004Keywords:
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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