On the geometric properties of the Bessel-Struve kernel function

TL;DR

This paper investigates the geometric properties of the Bessel-Struve kernel function, focusing on conditions for close-to-convexity and starlikeness within the unit disk, contributing to the understanding of its complex geometric behavior.

Contribution

It introduces the Bessel-Struve kernel function and establishes new sufficient conditions for its close-to-convexity and starlikeness in the unit disk.

Findings

Conditions for close-to-convexity of $\

Sufficient conditions for $z\mathcal{B}_\nu$ to be starlike.

Abstract

This paper introduce the Bessel-Struve kernel functions $\mathcal{B}_\nu$ defined on the unit disk in the complex plane. We studies the close-to-convexity of $\mathcal{B}_\nu$ with respect to several starlike functions. Sufficient condition on $\nu$ for which the function $z\mathcal{B}_\nu$ is starlike is given.