On the classes of higher-order Jensen-convex functions and Wright-convex functions

TL;DR

This paper compares classes of higher-order Jensen-convex and Wright-convex functions, establishing subclass relationships for odd natural numbers using new measure-theoretic tools.

Contribution

It introduces measure-theoretic tools to analyze and compare higher-order convex function classes, revealing subclass relationships for odd n.

Findings

n-Wright-convex functions form a proper subclass of n-Jensen-convex functions for odd n

New measure-theoretic tools are developed for this analysis

The relationship between these convex function classes is clarified

Abstract

The classes of n-Wright-convex functions and n-Jensen-convex functions are compared with each other. It is shown that for any odd natural number $n$ the first one is the proper subclass of the second one. To reach this aim new tools connected with measure theory are developed.