On some geometric properties of the Le Roy-type Mittag-Leffler function

In this paper, we consider the Le Roy-type Mittag-Leffler function. Our main focus is to establish some sufficient conditions so that the normalized Le-Roy type Mittag-Leffler function posses some geometric properties such as starlikeness, convexity, close-to-convexity insert ignore into journalissuearticles values(univalency); and uniformly convexity inside the unit disk. Using these results, geometric properties of the normalized Mittag-Leffler function are derived as application. Results obtained in this paper are new. Interesting consequences, corollaries and examples are provided to support that these results are better and improve several results available in the literature.