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

Authors : Evrim TOKLU

Pages : 2610-2630

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper we deal with the radii of starlikeness and convexity of the $q$-Mittag-Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-P\`olya class of real entire functions plays a pivotal role in this investigation.
Keywords : q Mittag Leffler functions, univalent, starlike and convex functions, radius of starlikeness and convexity, Laguerre P`olya class of entire functions