Coefficient Estimates and Fekete–Szegö Functional Inequalities for a Certain Subclass of Analytic and Bi-Univalent Functions

Abstract

The present paper introduces a new class of bi-univalent functions defined on a symmetric domain using Gegenbauer polynomials. For functions in this class, we have derived the estimates of the Taylor–Maclaurin coefficients, a2 and a3, and the Fekete-Szegö functional. Several new results follow upon specializing the parameters involved in our main results.

New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q-Calculus

“…A new family of holomorphic and bi-univalent functions is introduced using a new operator joining Poisson distribution with a Ruscheweyh derivative operator and upper bounds for the second and third coefficients are discussed in [17]. Other similar very recent studies can be seen in [18][19][20].…”

Initial Coefficients Estimates and Fekete–Szegö Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination

“…The solution of this problem is of great interest in the geometric function theory. In the literature, there is a huge amount of results for several classes of functions that deal with the solution of the Fekete-Szegö problem (see, [32][33][34][35][36][37][38][39]).…”

Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials

“…All studies aim to determine more accurate estimations on the coefficients of these functions. Certain subclasses of the bi-univalent functions were identified based on specific properties and or conditions that enable more precise evaluations of their coefficients (see [26][27][28][29][30][31][32][33]). In this article, we consider a particular subclass of the bi-univalent functions subordinate to GPs to derive upper bounds for the Taylor-Maclaurin coefficients, | a 2 | and | a 3 |, and determine the greatest value of the Fekete-Szegö functional F η ( f ).…”