Subordination Involving Gauss Hypergeometric Function

TL;DR

This paper establishes new sufficient conditions for the normalized Gauss hypergeometric function to exhibit exponential starlikeness, convexity, and Janowski properties within the unit disk, using differential subordination techniques.

Contribution

It introduces novel parameter conditions ensuring geometric properties of the hypergeometric function, expanding understanding of its behavior in complex analysis.

Findings

Derived conditions for exponential starlikeness and convexity.

Established parameter criteria for Janowski convexity and starlikeness.

Presented several new consequences illustrating the results.

Abstract

The primary objective of this work is to obtain some sufficient conditions so that normalized Gauss hypergeometric function satisfies exponential starlikeness and convexity in the unit disk. Moreover, conditions on parameter of this function has been derived for being Janowski convexity and starlikeness with the help of differential subordination. Results established in this work are presumably new and their significance is illustrated by several consequences.