Popoviciu's type inequalityies for h-MN-convex functions

TL;DR

This paper establishes new Popoviciu-type inequalities for h-MN-convex functions, involving various mean combinations and properties of the function h, expanding the theoretical framework of convexity inequalities.

Contribution

It introduces novel inequalities for h-MN-convex functions, generalizing existing convexity inequalities with new mean and function conditions.

Findings

Proved inequalities for h-MN-convex functions involving arithmetic, geometric, and harmonic means.

Extended classical Popoviciu inequalities to a broader class of convex functions.

Demonstrated the applicability of superadditive and subadditive properties of h in inequality proofs.

Abstract

In this work, several inequalities of Popoviciu type for h-MN-convex functions are proved, where M or N are denote to Arithmetic, Geometric and Harmonic means and $h$ is a non-negative superadditive or subadditive function.