Analytic Function Classes Defined by Mittag–Leffler Inspired Poisson-Type Series

Abstract

In this article, we introduce new subclass s𝑚 𝛼,𝛽,𝜆(𝛾) of univalent functions based on Mittag-Leffler function related to the distribution series within the unit disc U = {𝜁 ∈ 𝐶 ∶ |𝜁| < 1}. Further the fundamental properties such as growth, distortion, extreme points, convexity, close-to-convexity, starlike and coefficient inequalities have been estimated for the subclass. In addition, we consider an integral means of inequality for the subclass. This work bridges the gap between fractional integral operators and Poisson distribution series by incorporating both into a new subclass of univalent functions. This integrative approach provides the valuable insights into the applications of geometric function theory in signal and image processing.