Some Characterizations on the Normalized Lommel, Struve and Bessel Functions of the First Kind

Abstract

In this paper, we introduce new technique for determining some necessary and sufficient conditions of the normalized Bessel functions $j_{\nu}$, normalized Struve functions $h_{\nu}$ and normalized Lommel functions $s_{\mu,\nu}$ of the first kind, to be in the subclasses of starlike and convex functions of order $\alpha$ and type $\beta$.