Mittag-Leffler Poisson Distribution Series and Their Application to Univalent Functions

Abstract

In this study, we establish a significant connection between certain subclasses of complex order univalent functions and the Mittag-Leffler-type Poisson distribution series. We provide criteria for these series to belong to the specific subclasses. The primary goal of this investigation is to derive necessary and sufficient conditions for the Mittag-Leffler-type Poisson distribution series $\mathcal{P}(p,u,v)(z)$ to be included in the classes $\mathcal{S}(\delta ,\eta ,\tau )$ and $\mathcal{R}(\delta ,\eta ,\tau )$. These findings enhance our understanding of the structural properties of univalent functions and extend the applicability of Mittag-Leffler-type distributions in complex analysis.