Some geometric properties of certain class of Le Roy type functions

Abstract

The main goal of this paper is to obtain sufficient conditions so that Le Roy type functions and multivariate Le Roy type functions satisfy subordination of exponential function. Moreover conditions on parameters have been derived to claim them being exponential starlike and exponential convex for both of the functions. Starlikeness, convexity and close-to-convexity have also been studied for multivariate Le Roy type functions. Results developed in this work are presumably new and their significance is illustrated by several consequences, graphical representations and examples.

23 pages