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

Nesar Hossain; Syed Abdul Mohiuddine

Makale detayları

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

Yazarlar:

Nesar Hossain | Syed Abdul Mohiuddine

Yayıncı:

Ankara University

Ana Başlıklar:

Operator Algebras and Functional Analysis

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 2, pp.277-293

Belge Tipi:

Makale

Yayın Tarihi:

6/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001348170

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

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

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

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

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

Makale detayları

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

Yazarlar:

Nesar Hossain | Syed Abdul Mohiuddine

Yayıncı:

Ankara University

Ana Başlıklar:

Operator Algebras and Functional Analysis

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 2, pp.277-293

Belge Tipi:

Makale

Yayın Tarihi:

6/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001348170

pISSN:

1303-5991

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

Sayı

Makale detayları

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

Yazarlar: Nesar Hossain | Syed Abdul Mohiuddine

Yayıncı: Ankara University

Ana Başlıklar: Operator Algebras and Functional Analysis

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 2, pp.277-293

Belge Tipi: Makale

Yayın Tarihi: 6/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001348170

pISSN: 1303-5991

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

Sayı

Yazarlar:

Nesar Hossain | Syed Abdul Mohiuddine

Yayıncı:

Ankara University

Ana Başlıklar:

Operator Algebras and Functional Analysis

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 2, pp.277-293

Belge Tipi:

Makale

Yayın Tarihi:

6/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001348170

pISSN:

1303-5991