Radii problems for the generalized Mittag-Leffler functions

Abstract

In this paper our aim is to investigate the radii of $\eta -$uniformly convexity, $\alpha -$convexity, $\eta -$parabolic starlikeness and strong starlikeness of order $\rho$ of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic. The basic tool of this study is the Mittag-Leffler function in series. Also we have shown that the obtained radii are the smallest positive roots of some functional equations.

arXiv admin note: text overlap with arXiv:1412.2000, arXiv:1801.08684, arXiv:1710.09715, arXiv:1702.00631 by other authors