Some te-univalent function subfamilies linked to generalized bivariate Fibonacci polynomials

Our present investigation is primarily motivated by the broad and impactful applications of special polynomials in geometric function theory. In particular, the generalized bivariate Fibonacci polynomials have recently attracted attention in the study of bi-univalent functions. In this article, we introduce and investigate a comprehensive subclass of Te-univalent functions, a recent development in geometric function theory, characterized by generalized bivariate Fibonacci polynomials. This polynomial sequence is chosen due to its flexibility, as numerous other polynomial families can be derived through appropriate specialization of its parameters. By applying the subordination technique, we derive bounds for the initial coefficients of functions belonging to this subfamily and investigate the associated Fekete–Szegö problem. In addition to presenting several new findings, we also explore meaningful connections with previously established results in the theory of bi-univalent and subordinate functions, thereby extending and unifying existing literature in a novel direction.