Fekete-Szegö Functional of a Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials (European Journal of Pure and Applied Mathematics, 2024)
In this paper, we introduce and investigate a class of bi-univalent functions, denoted by $\mathcal{F}(n, α, β)$, 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-Szegö inequality of functions belonging to this class.
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\