Convolution of Convex Functions

Abstract

In this thesis, we investigate convex sets, convex functions, the continuity and differentiability of convex functions, and their characteristics. After studying these results, we review the research paper of the title “On the convolution and subordination of convex function” and offer some new results. It is demonstrated that convolution with a prestarlike function of the same order results in the closure of the class of convex functions of order α. Our proof shows that subordination is preserved when a prestarlike function of the same order is convolutioned with a convex function of order α. For the family of convex functions, we also find a subordinating factor sequence .