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    Exploration of New Classes of Bi-univalent Functions Defined by the Subordination Principle Using q-Gegenbauer Polynomials
    (Springer, 2024) Alsoboh, Abdullah; Amourah, Ala; Alatawi, Maryam Salem; Gharib, Gharib; Sakar, Fethiye
    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.