# A Study on \(\mathcal{I}\)-localized Sequences in \(S\)-metric Spaces

## DOI:

https://doi.org/10.26713/cma.v14i1.2056## Keywords:

Ideal, S-metric space, I-locator, I-localized sequence, I*-localized sequence, 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. Finally, we use this idea for an \(\mathcal{I}\)-localized sequence to be \(\mathcal{I}\)-Cauchy when the ideal \(\mathcal{I}\) satisfies the condition (*AP*).

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*Communications in Mathematics and Applications*,

*14*(1), 49–58. https://doi.org/10.26713/cma.v14i1.2056

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