  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.
