A study on $\mathcal I$-localized sequences in S-metric spaces

TL;DR

This paper explores the concepts of $\\mathcal{I}$-localized sequences and related properties in $S$-metric spaces, providing new insights into their behavior and introducing the idea of an $\\mathcal{I}$-barrier.

Contribution

It introduces and analyzes the notions of $\\mathcal{I}$-localized and $\\mathcal{I^*}$-localized sequences in $S$-metric spaces, expanding the theoretical framework.

Findings

Characterization of $\\mathcal{I}$-localized sequences

Properties of $\\mathcal{I}$-Cauchy sequences in $S$-metric spaces

Introduction of the concept of $\\mathcal{I}$-barrier

Abstract

In this paper we study the notion of $\mathcal{I}$-localized and $\mathcal{I^*}$-localized sequences in $S$-metric spaces. Also, we investigate some properties related to $\mathcal{I}$-localized and $\mathcal{I}$-Cauchy sequences and give the idea of $\mathcal{I}$-barrier of a sequence in the same space.