Radii problems for the generalized Mittag-Leffler functions
J. Korean Math. Soc. 2020 Vol. 57, No. 4, 1031-1052
Published online July 1, 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 $\rho$, entire functions, real zeros, Weierstrassian decomposition
MSC numbers : Primary 30C45, 30C15; Secondary 33E12
Supported by : This work was supported by INSPIRE fellowship, Department of Science and Technology, New Delhi, Government of India.
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