Necessity and sufficiency for hypergeometric functions to be in a subclass of analytic functions

Abstract

The purpose of this paper is to introduce necessary and sufficient condition of (Gaussian) hypergeometric functions to be in a subclass of uniformly starlike and uniformly convex functions. Operators related to hypergeometric functions are also considered. Some of our results correct previously known results.

Keywords

• Univalent
• Starlike
• Convex
• Uniformly starlike
• Uniformly convex
• Hypergeometric function