An elementary proof for the decomposition theorem of Wright convex functions

TL;DR

This paper provides a straightforward, elementary proof of the decomposition theorem for Wright convex functions, avoiding complex transfinite methods previously used in the literature.

Contribution

It offers a new, simpler proof of the decomposition theorem for Wright convex functions without relying on advanced transfinite tools.

Findings

Elementary proof of the decomposition theorem established

Avoids use of transfinite tools and complex theorems

Simplifies understanding of Wright convex functions

Abstract

The main goal of this paper is to give a completely elementary proof for the decomposition theorem of Wright convex functions which was discovered by C.\ T.\ Ng in 1987. In the proof, we do not use transfinite tools, i.e., variants of Rod\'e's theorem, or de Bruijn's theorem related to functions with continuous differences.