A study of bi-univalent functions associated with the modified Tremblay operator and Horadam polynomials

Subclasses of bi-univalent functions defined by the modified Tremblay operator and the Horadam polynomial generating function are investigated. Motivated by recent developments in geometric function theory, two subclasses are introduced through suitable subordination conditions involving the modified Tremblay operator. The principal objective is to derive estimates for the initial Taylor coefficients and the corresponding Fekete-Szego inequalities associated with these subclasses. The obtained results are established by employing suitable analytical techniques together with standard results from the theory of functions with positive real part. Furthermore, several consequences of the main results are presented by assigning appropriate values to the parameters appearing in the defining conditions, leading to interesting special cases. The study extends existing investigations by combining the modified Tremblay operator with the Horadam polynomial generating function within the framework of bi-univalent function theory. The obtained coefficient estimates and Fekete-Szego inequalities provide further insight into subclasses of bi-univalent functions defined through the modified Tremblay operator and the Horadam polynomial generating function.