Exploring Fekete-Szegő inequalities for an admissible class of bi-univalent functions involved Gegenbauer polynomials

Abstract

This paper presents a newly defined subclass of bi-univalent functions linked to the Genenbauer polynomial. The functions in this subclass satisfy specific subordination conditions within a symmetric domain inside the open unit disk. For this subclass, we derive bounds for the Taylor-Maclaurin coefficients [Formula: see text] [Formula: see text] and the Fekete-Szegő functional [Formula: see text] The existing method has been extended to produce additional bi-univalent subfamilies as well as other special functionalities.

Keywords

• Analytic functions
• bi-univalent functions
• Fekete-Szegő problem
• Gegenbauer polynomial
• subordination
• 30C45