Radii problems for the generalized Mittag-Leffler functions
Abstract
In this paper our aim is to investigate the radii of η-uniformly convexity, α-convexity, η-parabolic starlikeness and strong starlikeness of order 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.
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