Deferred statistical convergence of sequences in octonion-valued metric spaces

Selim Çetin; Ömer Kişi; Mehmet Gürdal

Makale detayları

Deferred statistical convergence of sequences in octonion-valued metric spaces

Yazarlar:

Selim Çetin | Ömer Kişi | Mehmet Gürdal

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 3, pp.375-394

Belge Tipi:

Makale

Yayın Tarihi:

9/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001357881

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 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.

 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.

 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.

 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.

Makale detayları

Deferred statistical convergence of sequences in octonion-valued metric spaces

Yazarlar:

Selim Çetin | Ömer Kişi | Mehmet Gürdal

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 3, pp.375-394

Belge Tipi:

Makale

Yayın Tarihi:

9/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001357881

pISSN:

1303-5991

Deferred statistical convergence

invariant

prime numbers

octanion metric space

Sayı

Makale detayları

Deferred statistical convergence of sequences in octonion-valued metric spaces

Yazarlar: Selim Çetin | Ömer Kişi | Mehmet Gürdal

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 3, pp.375-394

Belge Tipi: Makale

Yayın Tarihi: 9/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001357881

pISSN: 1303-5991

Deferred statistical convergence

invariant

prime numbers

octanion metric space

Sayı

Yazarlar:

Selim Çetin | Ömer Kişi | Mehmet Gürdal

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 3, pp.375-394

Belge Tipi:

Makale

Yayın Tarihi:

9/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001357881

pISSN:

1303-5991