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

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

2 Department of Mathematics, Faculty of Science, Menofia University, Shebin Elkom 32511, Egypt

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