RADIUS OF STARLIKENESS AND HARDY SPACE OF MITTAG-LEFFLER FUNCTIONS

Abstract

In the present work, Mittag-Leffler functions with its normalization are considered. Several results are obtained so that these functions have certain geometric properties including starlikeness, convexity, close-to-convexity of order α and radius of starlikeness of order α. Furthermore, we obtain condition so that the normalized Mittag-Leffler functions belongs to the Hardy space and to the class of bounded analytic functions. Results obtained are new and their usefulness are depicted by deducing several interesting corollaries and examples.