Convex Functions and Exponential Convexity

Abstract

One of the impressive application of the theory of convex functions is to the study of classical inequalities. Here, we show that how the theory provides an elementary, elegant, and unifed treatment of some of the best known inequalities in mathematics. The goal of this study is to give a short summary of the main results of the Hermite- Hadamard inequality for AG-convex functions, which are a special type of convex functions that the author has been studying for the past year. Also we present some interesting nontrivial examples to support our inequalities. Furthermore, we focus on exponentially convex functions and establish some important results equipped with integration, we also present some examples to support our main results.