One some differential subordination involving the Bessel-Struve kernel function

TL;DR

This paper investigates the inclusion properties of the Bessel-Struve kernel functions within the Janowski class, establishing conditions for their mapping to the right half-plane and exploring differential subordinations.

Contribution

It introduces new conditions for Bessel-Struve kernel functions to belong to the Janowski class and analyzes their differential subordination properties.

Findings

Conditions for Bessel-Struve kernel to map the unit disk to the right half-plane

Derivation of differential subordination involving the Bessel-Struve kernel

Use of recurrence relations to establish main results

Abstract

In this article we study the inclusion properties of the Bessel-Struve kernel functions in the Janowski class. In particular, we find the conditions for which the Bessel-Struve kernel functions maps the unit disk to right half plane. An open problem in this aspect are also given. The third order differential subordination involving the Bessel-Struve kernel is also considered. The results are derived by defining suitable classes of admissible functions. One of the recurrence relation of the Bessel-Struve kernel play an important role to derive the main results.