On the geometric properties of the Bessel-Struve kernel function

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.