Petrovic's type inequality for exponentially convex functions and coordinated exponentially convex functions

Abstract

In this paper, we produce a novel framework of a subclass of convex functions that is exponentially convex functions. Moreover, it is observed that the new concept helps to build new inequalities of Petrovic’s ´ type by employing exponentially convex functions. We also introduce the idea of coordinated exponentially convex functions and derive Petrovic’s ´ type inequality for coordinated exponentially convex functions. We also find Lagrange type and Cauchy type mean value theorems for Petrovic’s ´ type inequality for exponentially convex and coordinated exponentially convex functions. Our consequences with this new generalizations has the abilities to be implemented for the evaluation of many mathematical problems.