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

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...

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Bibliographic Details
Published in:Communications in Mathematics and Applications 2023-05, Vol.14 (1), p.49-58
Main Authors: Banerjee, Amar Kumar, Hossain, Nesar
Format: Article
Language:English
Subjects:
Codes
Mathematics
Metric space
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Summary: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).
ISSN:0976-5905
0975-8607
DOI:10.26713/cma.v14i1.2056