Journal of the
Korean Mathematical Society JKMS

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 functi

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.