ON \(\lambda\)-WEAK CONVERGENCE OF SEQUENCES DEFINED BY AN ORLICZ FUNCTION
In this article, we introduce and rigorously analyze the concept of difference \(\lambda\)-weak convergence for sequences defined by an Orlicz function. This notion generalizes the classical weak convergence by incorporating a \(\lambda\)-density framework and an Orlicz function, providing a more fl...
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| Format: | Article |
| Language: | English |
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2025-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/875 |
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| author | Ömer Kişi Mehmet Gürdal |
| author_facet | Ömer Kişi Mehmet Gürdal |
| author_sort | Ömer Kişi |
| collection | DOAJ |
| description | In this article, we introduce and rigorously analyze the concept of difference \(\lambda\)-weak convergence for sequences defined by an Orlicz function. This notion generalizes the classical weak convergence by incorporating a \(\lambda\)-density framework and an Orlicz function, providing a more flexible tool for analyzing convergence behavior in sequence spaces. We systematically investigate the algebraic and topological properties of these newly defined sequence spaces, establishing that they form linear and normed spaces under suitable conditions. Our results include demonstrating the convexity of these spaces and identifying several important inclusion relationships among them, such as strict inclusions between spaces involving different orders of difference operators and Orlicz functions satisfying the \(\Delta_{2}\)-condition. |
| format | Article |
| id | doaj-art-3bcf065f68484e3cba1a29cfd6483d25 |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-3bcf065f68484e3cba1a29cfd6483d252025-08-20T03:34:33ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522025-07-0111110.15826/umj.2025.1.006230ON \(\lambda\)-WEAK CONVERGENCE OF SEQUENCES DEFINED BY AN ORLICZ FUNCTIONÖmer Kişi0Mehmet Gürdal1Department of Mathematics, Bartin University, 74110 BartınDepartment of Mathematics, Suleyman Demirel University, 32260 IspartaIn this article, we introduce and rigorously analyze the concept of difference \(\lambda\)-weak convergence for sequences defined by an Orlicz function. This notion generalizes the classical weak convergence by incorporating a \(\lambda\)-density framework and an Orlicz function, providing a more flexible tool for analyzing convergence behavior in sequence spaces. We systematically investigate the algebraic and topological properties of these newly defined sequence spaces, establishing that they form linear and normed spaces under suitable conditions. Our results include demonstrating the convexity of these spaces and identifying several important inclusion relationships among them, such as strict inclusions between spaces involving different orders of difference operators and Orlicz functions satisfying the \(\Delta_{2}\)-condition.https://umjuran.ru/index.php/umj/article/view/875weak convergence, orlicz function, λ convergence. |
| spellingShingle | Ömer Kişi Mehmet Gürdal ON \(\lambda\)-WEAK CONVERGENCE OF SEQUENCES DEFINED BY AN ORLICZ FUNCTION Ural Mathematical Journal weak convergence, orlicz function, λ convergence. |
| title | ON \(\lambda\)-WEAK CONVERGENCE OF SEQUENCES DEFINED BY AN ORLICZ FUNCTION |
| title_full | ON \(\lambda\)-WEAK CONVERGENCE OF SEQUENCES DEFINED BY AN ORLICZ FUNCTION |
| title_fullStr | ON \(\lambda\)-WEAK CONVERGENCE OF SEQUENCES DEFINED BY AN ORLICZ FUNCTION |
| title_full_unstemmed | ON \(\lambda\)-WEAK CONVERGENCE OF SEQUENCES DEFINED BY AN ORLICZ FUNCTION |
| title_short | ON \(\lambda\)-WEAK CONVERGENCE OF SEQUENCES DEFINED BY AN ORLICZ FUNCTION |
| title_sort | on lambda weak convergence of sequences defined by an orlicz function |
| topic | weak convergence, orlicz function, λ convergence. |
| url | https://umjuran.ru/index.php/umj/article/view/875 |
| work_keys_str_mv | AT omerkisi onlambdaweakconvergenceofsequencesdefinedbyanorliczfunction AT mehmetgurdal onlambdaweakconvergenceofsequencesdefinedbyanorliczfunction |