A Study on Nθ-Quasi-Cauchy Sequences

Abstract EN

Recently, the concept of Nθ-ward continuity was introduced and studied.

In this paper, we prove that the uniform limit of Nθ-ward continuous functions is Nθ-ward continuous, and the set of all Nθ-ward continuous functions is a closed subset of the set of all continuous functions.

We also obtain that a real function f defined on an interval E is uniformly continuous if and only if (f(αk)) is Nθ-quasi-Cauchy whenever (αk) is a quasi-Cauchy sequence of points in E.