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

Evrim Toklu

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arXiv · 1907.04636

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

Evrim Toklu

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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.

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Evrim Toklu. 2019-07-10. Radii of starlikeness and convexity of $q-$Mittag--Leffler functions. https://arxiv.org/abs/1907.04636

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