Exponential starlikeness and convexity of confluent hypergeometric, Lommel and Struve functions

TL;DR

This paper establishes conditions under which certain special functions, including Lommel, Struve, and confluent hypergeometric functions, exhibit exponential convexity and starlikeness within the open unit disk, using differential subordination.

Contribution

It provides new sufficient conditions for exponential convexity and starlikeness of these functions, employing the method of differential subordination.

Findings

Conditions for exponential convexity of Lommel, Struve, and hypergeometric functions.

Conditions for exponential starlikeness of these functions.

Illustrative examples demonstrating the results.

Abstract

Sufficient conditions are obtained on the parameters of Lommel function of the first kind, generalized Struve function of the first kind and the confluent hypergeometric function under which these special functions become exponential convex and exponential starlike in the open unit disk. The method of differential subordination is employed in proving the results. Few examples are also provided to illustrate the results obtained.