Radii of starlikeness and convexity of q -Mittag-Leffler functions

Abstract

In this paper we deal with the radii of starlikeness and convexity of the q -Mittag–Leffler function forthree different kinds of normalization by making use of their Hadamard factorization in such a way that the resultingfunctions are analytic in the unit disk of the complex plane. By applying Euler–Rayleigh inequalities for the first positivezeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. TheLaguerre–Pólya class of real entire functions plays a pivotal role in this investigation.