On relations between some types of convex functions

Abstract

In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $\phi $-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by superquadratic functions and how to adapt the technique used to get them in order to obtain new results satisfied by uniformly convex functions and to $\phi $-convex functions. Also, we show examples that emphasize relations between superquadracity and some other types of convex functions