- Turkish Journal of Mathematics
- Vol: 43 Issue: 5
- Radii of starlikeness and convexity of $q$-Mittag-Leffler functions
Radii of starlikeness and convexity of $q$-Mittag-Leffler functions
Authors : Evrim Toklu
Pages : 2610-2630
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Publication Date : 9999-12-31
Article Type : Makaleler
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