New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences
This paper explores the concepts of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical lim...
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2025-01-01
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| author | María C. Listán-García Ömer Kişi Mehmet Gürdal |
| author_facet | María C. Listán-García Ömer Kişi Mehmet Gürdal |
| author_sort | María C. Listán-García |
| collection | DOAJ |
| description | This paper explores the concepts of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical limit points, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical cluster points, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical Cauchy multiset sequences. Building upon previous work in the field, we investigate the relationships between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical convergence and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="fraktur">J</mi><mo>*</mo></msup></semantics></math></inline-formula>-lacunary statistical convergence in multiset sequences. The findings contribute to a deeper understanding of the convergence behaviour of multiset sequences and provide new insights into the application of ideal convergence in this context. |
| format | Article |
| id | doaj-art-d9c63a4642fd47c99cbbdcfff6b40a54 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-d9c63a4642fd47c99cbbdcfff6b40a542025-01-10T13:18:28ZengMDPI AGMathematics2227-73902025-01-0113116410.3390/math13010164New Perspectives on Generalised Lacunary Statistical Convergence of Multiset SequencesMaría C. Listán-García0Ömer Kişi1Mehmet Gürdal2Department of Mathematics, Faculty of Science, University of Cádiz, 11510 Cádiz, SpainDepartment of Mathematics, Bartin University, 74100 Bartın, TurkeyDepartment of Mathematics, Süleyman Demirel University, 32260 Isparta, TurkeyThis paper explores the concepts of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical limit points, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical cluster points, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical Cauchy multiset sequences. Building upon previous work in the field, we investigate the relationships between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical convergence and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="fraktur">J</mi><mo>*</mo></msup></semantics></math></inline-formula>-lacunary statistical convergence in multiset sequences. The findings contribute to a deeper understanding of the convergence behaviour of multiset sequences and provide new insights into the application of ideal convergence in this context.https://www.mdpi.com/2227-7390/13/1/164multiset sequences\({\mathfrak{J}}\)-lacunary statistical Cauchy\({\mathcal{I}^{\ast}}\)-lacunary statistical Cauchy\({\mathfrak{J}}\)-lacunary statistical limit point\({\mathfrak{J}}\)-lacunary statistical cluster point |
| spellingShingle | María C. Listán-García Ömer Kişi Mehmet Gürdal New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences Mathematics multiset sequences \({\mathfrak{J}}\)-lacunary statistical Cauchy \({\mathcal{I}^{\ast}}\)-lacunary statistical Cauchy \({\mathfrak{J}}\)-lacunary statistical limit point \({\mathfrak{J}}\)-lacunary statistical cluster point |
| title | New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences |
| title_full | New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences |
| title_fullStr | New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences |
| title_full_unstemmed | New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences |
| title_short | New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences |
| title_sort | new perspectives on generalised lacunary statistical convergence of multiset sequences |
| topic | multiset sequences \({\mathfrak{J}}\)-lacunary statistical Cauchy \({\mathcal{I}^{\ast}}\)-lacunary statistical Cauchy \({\mathfrak{J}}\)-lacunary statistical limit point \({\mathfrak{J}}\)-lacunary statistical cluster point |
| url | https://www.mdpi.com/2227-7390/13/1/164 |
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