On generalized difference $\mathscr{I}$-convergent sequences in neutrosophic $n$-normed linear spaces

Year 2025, Volume: 74 Issue: 2, 277 - 293, 19.06.2025

Nesar Hossain , Syed Abdul Mohiuddine

https://doi.org/10.31801/cfsuasmas.1566187

Abstract

In this article, we delve into the intricate concepts of $\Delta^m\mathscr{I}$-convergence and $\Delta^m\mathscr{I}$-Cauchy sequences within neutrosophic $n$-normed linear spaces, unveiling several intriguing properties. Our findings establish that every neutrosophic $n$-normed linear space is $\Delta^m\mathscr{I}$-complete. We also thoroughly investigate the $\Delta^m\mathscr{I}$-limit and $\Delta^m\mathscr{I}$-cluster points of sequences in relation to the neutrosophic $n$-norm, proving that the set of all $\Delta^m\mathscr{I}$-cluster points forms a closed set under the topology induced by the neutrosophic $n$-norm. Additionally, we demonstrate that a linear operator preserves $\Delta^m\mathscr{I}$-convergence if and only if it remains continuous with respect to the neutrosophic $n$-norm.

Keywords

Neutrosophic $n$-normed linear space, $\Delta^m\mathscr{I}(\mathscr{N}_n)$-convergence, $\Delta^m\mathscr{I}(\mathscr{N}_n)$-completeness, $\Delta^m\mathscr{I}^*(\mathscr{N}_n)$-convergence, $\Delta^m\mathscr{I}(\mathscr{N}_n)$-limit point, $\mathscr{N}_n$-continuous mapping

Ethical Statement

Not applicable

Project Number

Not applicable

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