Exploration of New Classes of Bi-univalent Functions Defined by the Subordination Principle Using q-Gegenbauer Polynomials

In this study, we introduce a new class of bi-univalent functions constructed using q-Gegenbauer polynomials. We analyze and characterize this newly defined class of functions, and derive estimates for the Taylor-Maclaurin coefficients |a2| and |a3|. Additionally, we investigate the formulation of functional problems specific to functions within this subclass, namely a3-σa22 (commonly known as the Fekete-Szegö problem). By systematically exploring parameter specialization, we discover a range of novel outcomes that shed light on various aspects of our main results, contributing to a broader understanding of the mathematical landscape under investigation. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.