UNIVALENT FUNCTION SUBCLASSES DEFINED VIA A NEW EXTENSION OF THE SALAGEAN OPERATOR

Abstract

Geometric function theory (GFT), a fundamental area in complex analysis, investigates the geometric behavior of analytic functions and has extensive applications in areas such as special functions, probability distributions, dynamical systems, fractional calculus, and analytic number theory. In this paper, we introduce a new generalized differential operator  defined on the open unit disk . Using this operator, we construct two new subclasses of univalent functions denoted by  and  and study their geometric and analytic properties. In particular, we establish coefficient estimates, inclusion relationships, and sufficient conditions for close-to-convexity. These findings contribute to the ongoing development of operator-based methods in GFT and provide a framework for further exploration of univalent function classes.