Deferred statistical convergence of sequences in octonion-valued metric spaces

Selim Çetin; Ömer Kişi; Mehmet Gürdal

doi:10.31801/cfsuasmas.1611730

Deferred statistical convergence of sequences in octonion-valued metric spaces

Abstract

By employing octonions, which offer a higher-dimensional and non-associative algebraic structure, octonion-valued metric spaces generalize conventional metric spaces. Every ring forms a module over itself, and every field forms a vector space over itself, as is commonly known. It should be noted, nevertheless, that octonions do not form a module over themselves and so cannot even be regarded as a ring because they lack the multiplicative union condition. The metric spaces we have defined and the findings produced in these spaces are very intriguing because of this aspect. Consequently, various conclusions pertaining to summability theory are examined utilizing some essential concepts associated with these mathematical structures. In particular, we present the concepts of deferred statistical convergence and deferred strong Cesàro summability in octonion-valued metric spaces and explore the connections between them. Additionally, we introduce and discuss the concepts of strong deferred invariant convergence, deferred invariant convergence in octonion-valued metric spaces, and deferred invariant statistical convergence.

Keywords

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Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Selim Çetin
0000-0002-9017-1465
Türkiye

Ömer Kişi
0000-0001-6844-3092
Türkiye

Mehmet Gürdal ^*
0000-0003-0866-1869
Türkiye

Publication Date

September 23, 2025

Submission Date

January 2, 2025

Acceptance Date

April 15, 2025

Published in Issue

Year 2025 Volume: 74 Number: 3

DOI

https://doi.org/10.31801/cfsuasmas.1611730

IZ

https://izlik.org/JA36BA23ZS

Cite

RIS / Bibtex

APA

Çetin, S., Kişi, Ö., & Gürdal, M. (2025). Deferred statistical convergence of sequences in octonion-valued metric spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 74(3), 375-394. https://doi.org/10.31801/cfsuasmas.1611730

AMA

1.Çetin S, Kişi Ö, Gürdal M. Deferred statistical convergence of sequences in octonion-valued metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74(3):375-394. doi:10.31801/cfsuasmas.1611730

Chicago

Çetin, Selim, Ömer Kişi, and Mehmet Gürdal. 2025. “Deferred Statistical Convergence of Sequences in Octonion-Valued Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 (3): 375-94. https://doi.org/10.31801/cfsuasmas.1611730.

EndNote

Çetin S, Kişi Ö, Gürdal M (September 1, 2025) Deferred statistical convergence of sequences in octonion-valued metric spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 3 375–394.

IEEE

[1]S. Çetin, Ö. Kişi, and M. Gürdal, “Deferred statistical convergence of sequences in octonion-valued metric spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 74, no. 3, pp. 375–394, Sept. 2025, doi: 10.31801/cfsuasmas.1611730.

ISNAD

Çetin, Selim - Kişi, Ömer - Gürdal, Mehmet. “Deferred Statistical Convergence of Sequences in Octonion-Valued Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74/3 (September 1, 2025): 375-394. https://doi.org/10.31801/cfsuasmas.1611730.

JAMA

1.Çetin S, Kişi Ö, Gürdal M. Deferred statistical convergence of sequences in octonion-valued metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74:375–394.

MLA

Çetin, Selim, et al. “Deferred Statistical Convergence of Sequences in Octonion-Valued Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 74, no. 3, Sept. 2025, pp. 375-94, doi:10.31801/cfsuasmas.1611730.

Vancouver

1.Selim Çetin, Ömer Kişi, Mehmet Gürdal. Deferred statistical convergence of sequences in octonion-valued metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025 Sep. 1;74(3):375-94. doi:10.31801/cfsuasmas.1611730

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