Geometric properties of normalized Le Roy-type Mittag-Leffler functions

Abstract

The main focus of the present paper is to establish sufficient conditions for the parameters of the normalized form of the generalized Le Roy-type Mittag-Leffler function have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disc. The results obtained are new and their usefulness is depicted by deducing several interesting corollaries. The results obtained improve some several results available in the literature for the Mittag-Leffler function.