Mapping properties of certain linear operator associated with hypergeometric functions

Abstract

The main object of the present paper is to nd some su¢ cient conditions in terms of hypergeometric inequalities so that the linear operator denoted by Ha;b;c : maps a certain subclass of close-to-convex function R (A;B) into subclasses of k-uniformly starlike and k-uniformly convex functions k 􀀀ST () and k 􀀀UCV() respectively. Further, we consider an integral operator and discuss its properties. Our results generalize some relevant results.