$\lambda$-statistically quasi-Cauchy sequences

TL;DR

This paper introduces and studies $mbda$-statistically quasi-Cauchy sequences, exploring their properties and the concept of $mbda$-statistically ward continuity, which relates to uniform continuity on certain compact sets.

Contribution

It defines $mbda$-statistically ward continuity and establishes its equivalence with uniform continuity on $mbda$-statistically ward compact subsets.

Findings

$mbda$-statistically ward continuity coincides with uniform continuity on $mbda$-statistically ward compact sets.

Introduces $mbda$-statistically quasi-Cauchy sequences as a new sequence type.

Provides characterization of functions preserving these sequences.

Abstract

The main object of this paper is to investigate $\lambda$-statistically quasi-Cauchy sequences. A real valued function $f$ defined on a subset $E$ of $\textbf{R}$, the set of real numbers, is called $\lambda$-statistically ward continuous on $E$ if it preserves $\lambda$-statistically quasi-Cauchy sequences of points in $E$. It turns out that uniform continuity coincides with $\lambda$-statistically ward continuity on $\lambda$-statistically ward compact subsets.