The double difference property for the class of locally H\"{o}lder continuous functions

TL;DR

This paper proves that pairs of locally Hölder continuous functions on the real line and the plane possess the double difference property, advancing understanding of their structural behavior.

Contribution

It establishes the double difference property for locally Hölder continuous functions on both d6 and d62, a novel result in the analysis of these function classes.

Findings

Locally Hölder continuous functions on d6 have the double difference property.

Locally Hölder continuous functions on d62 have the double difference property.

The property enhances understanding of the regularity and structure of these functions.

Abstract

In this paper, we show that the pair of classes of locally H\"{o}lder continuous functions (considered on $\mathbb{R}$ and $\mathbb{R}^{2}$, respectively) has the double difference property.