A NEW SUBCLASS OF ANALYTIC AND UNIVALENTFUNCTIONS ASSOCIATED WITH MITTAG-LEFFLERTYPE POISSON DISTRIBUTION OPERATOR

Abstract

The present work is concerned with the study of a new subclass
of analytic functions, T Mm α,ρ,φ(γ), defined in terms of negatively normalized Mittag-Leffler type functions. It establishes conditions under which these functions exhibit significant geometric properties such as starlikeness, convexity, close-to-convexity and boundedness of coefficients within the open unit disc D. The work further explores various function theoretic aspects, including extremal functions, sharp coefficient bounds, integral means inequalities and growth and distortion theorems. In addition, it examines the impact of certain integral operators on the structure of this function class. These results offer a unified framework that encompasses
several known subclasses and lays the groundwork for further research in eometric function theory, fractional calculus and operator theory.