Generalization of Popoviciu type inequalities for symmetric means generated by convex functions

Abstract

In this paper an inequality of Popoviciu, which was improved by Vasic and Stankovic [13], is generalized by using Green function. An extension of Popoviciu type inequality is introduced. The mean value theorems, nexponential convexity and exponential convexity are presented for the differences of these inequalities and related Cauchy means are also generated.