Maclaurin Coefficient Estimates for Bi‑Univalent Function Classes Generated by a Parameterized Integral Transformation

This paper introduces new subclasses of the bi-univalent function class , defined via a newly constructed integral operator denoted by ​, acting on analytic functions within the open unit disc . These subclasses are formulated based on multi-parameter operator structures that exhibit rich analytic behavior. We investigate the coefficient bounds associated with functions belonging to these classes, with particular focus on deriving sharp estimates for the first two Taylor–Maclaurin coefficients, namely . The findings contribute to the structural understanding of bi-univalent functions and offer new directions for application within the framework of geometric function theory.