Convexity, Starlikeness, and Prestarlikeness of Wright Functions

Abstract

This article deals with the normalized Wright function and its geometric properties. In particular, we find sufficiency criteria for close-to-convexity with respect to starlike function ς1−ς2. We also find conditions such that the normalized Wright function is starlike. The convexity along the imaginary axis and starlikeness of a certain order is also a part of our discussion. Moreover, we study the bounded turning of the partial sums and prestarlikeness of this function. We use positivity techniques to obtain these results.

Keywords

• starlike function
• prestarlike functions
• convexity along imaginary axis
• close-to-convex function
• Wright functions
• positivity techniques