Study of analytic function related to the Le Roy-type Mittag-Leffler function

K.  Mehrez

doi:10.37863/umzh.v75i5.7013

K. Mehrez Department of Mathematics, Kairouan Preparatory Institute for Engineering Studies, University of Kairouan, Tunisia

DOI: https://doi.org/10.37863/umzh.v75i5.7013

Keywords: Le Roy-type Mittag-leﬄer function, Analytic function, Univalent, starlike, convex, close-to-convex functions

Abstract

UDC 517.547

We study some geometric properties (such as univalence, starlikeness, convexity, and close-to-convexity) of Le Roy-type Mittag-Leffler function. In order to achieve our goal, we use new two-sided inequalities for the digamma function. Some examples are also provided to illustrate the obtained results. Interesting consequences are deduced to show that these results improve several results available in the literature for the two-parameter Mittag-Leffler function.

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