A Study on \(\mathcal{I}\)-localized Sequences in \(S\)-metric Spaces - Banerjee, Amar Kumar; Hossain, Nesar (Communications in Mathematics and Applications, 2023)
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).