Radii of starlikeness and convexity of Wright functions

Abstract

In this paper our aim is to find the radii of starlikeness and convexity of the normalized Wright functions for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for Wright function and properties of real zeros of Wright function and its derivative. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for  the normalized Wright functions. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind. Some open problems are also proposed, which may be of interest for further research.