Certain properties of bi-starlikeness and bi-convexity functions associated with Horadam polynomial defined through (p,q)-calculus

Abstract

In this research work, we explore the field of univalent analytic and bi-univalent functions, focusing on subclasses connected to Horadam polynomials. We introduce more generalized class that includes both bi-starlike and bi-convex functions. Our main objectives are to establish precise coefficient bounds and to derive Fekete-Szeg\"{o} inequalities for functions in the newly defined class. Additionally, we present detailed observations and special cases to demonstrate the breadth and significance of our findings.