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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| Main Authors: | , |
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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 |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/875 |
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| Summary: | 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. |
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| ISSN: | 2414-3952 |