A study on ideal ward continuity

TL;DR

This paper investigates the properties of ideal ward continuous functions, establishing conditions under which they are uniformly continuous and providing characterizations through ideal quasi-Cauchy sequences.

Contribution

It introduces new conditions for uniform continuity of ideal ward continuous functions and characterizes them via ideal quasi-Cauchy sequences.

Findings

Ideal ward continuous functions are uniformly continuous on certain sets.

Uniform continuity is characterized via ideal quasi-Cauchy sequences.

The paper provides conditions under which ideal ward continuous functions are uniformly continuous.

Abstract

In this paper, we prove that any ideal ward continuous function is uniformly continuous either on an interval or on an ideal ward compact subset of $\textbf{R}$. A characterization of uniform continuity is also given via ideal quasi-Cauchy sequences.