Radii problems for the generalized Mittag-Leffler functions
J. Korean Math. Soc.
Published online March 13, 2020
ANUJA PRAJAPATI
Sambalpur University
Abstract : In this paper our aim is to find various radii problems 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.
Keywords : Generalized Mittag-Leffler functions; radius of $\eta$uniformly convexity of order $\rho$; radius of $\alpha$convexity of order $\rho$; radius of $\eta$parabolic starlikeness of order $\rho$; radius of strong starlikeness of order $\rho$
MSC numbers : 30C45, 30C15 ; 33E12.
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