Remarks on Uniformly Symmetrically Continuous Functions

TL;DR

This paper introduces the concept of uniform symmetric continuity for functions on real subsets, explores its properties, compares it with related continuity notions, and provides characterizations and examples.

Contribution

It defines uniform symmetric continuity, investigates its properties, and distinguishes it from symmetric and uniform continuity with new characterizations.

Findings

Uniform symmetric continuity is a distinct continuity concept.

Characterizations of uniformly symmetrically continuous functions are established.

Several illustrative examples are provided.

Abstract

We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of symmetrically continuous functions and uniformly continuous functions. We obtain some characterizations of uniformly symmetrically continuous functions. Several examples are also given.