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http://dx.doi.org/10.4134/JKMS.j190571

RADII PROBLEMS FOR THE GENERALIZED MITTAG-LEFFLER FUNCTIONS  

Prajapati, Anuja (Department of Mathematics Sambalpur University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 1031-1052 More about this Journal
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;
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