Geometric and Functional Symmetries in q-Bernoulli Polynomial Generated Bi-Univalent Function Subfamilies

This study is inspired by the rich symmetry and diverse applications of special polynomial families, with a particular focus on the q-Bernoulli polynomials, which have recently emerged as significant tools in bi-univalent function theory. These polynomials are distinguished by their mathematical versatility, analytical manageability, and strong potential for generalization, offering an elegant framework for advancing the study of such functions. In this paper, we introduce a novel subclass of bi-univalent functions defined through q-Bernoulli polynomials. We obtain coefficient estimates for functions in this class and investigate their implications for the Fekete–Szegö functional. Additionally, we present several new results to enrich the theoretical landscape of bi-univalent functions associated with q-Bernoulli polynomials.