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





Ideal, S-metric space, I-locator, I-localized sequence, I*-localized sequence, I-barrier


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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Author Biography

Amar Kumar Banerjee, Department of Mathematics, The University of Burdwan, Golapbag, Burdwan 713104, West Bengal, India




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How to Cite

Banerjee, A. K., & Hossain, N. (2023). A Study on \(\mathcal{I}\)-localized Sequences in \(S\)-metric Spaces. Communications in Mathematics and Applications, 14(1), 49–58. https://doi.org/10.26713/cma.v14i1.2056



Research Article