A New Subclass of Bi-Univalent Functions Defined by Subordination to Laguerre Polynomials and the (p,q)-Derivative Operator

In this work, we introduce a new subclass of bi-univalent functions using the (p,q)-derivative operator and the concept of subordination to generalized Laguerre polynomials Ltς(k), which satisfy the differential equation ky″+(1+ς−k)y′+ty=0, with 1+ς>0, k∈R, and t≥0. We focus on functions that blend the geometric features of starlike and convex mappings in a symmetric setting. The main goal is to estimate the initial coefficients of functions in this new class. Specifically, we obtain sharp upper bounds for |a2| and |a3| and for the Fekete–Szegö functional |a3−ηa22| for some real number η. In the final section, we explore several special cases that arise from our general results. These results contribute to the ongoing development of bi-univalent function theory in the context of (p,q)-calculus.