Briot-Bouquet differential subordinations of analytic functions involving the Mittag-Leffler function defined in Cardioid domain

TL;DR

This paper introduces a new subclass of analytic functions involving the Mittag-Leffler function that map the unit disc onto a cardioid domain, and explores their properties through Briot-Bouquet differential subordinations.

Contribution

It establishes a novel function subclass based on Mittag-Leffler functions and applies differential subordination techniques to analyze their geometric properties.

Findings

Defined a new subclass of functions mapping to a cardioid domain

Applied Briot-Bouquet differential subordinations to this class

Extended the technique of Miller and Mocanu to this context

Abstract

In this researh work, we establish a new subclass of analytic functions constructed by the Mittag-Leffler function that maps the open unit disc onto the region bounded by the Cardioid domain. Using a technique introduced by Miller and Mocanu, we investigate several Briot-Bouquet differential subordinations for this function class.