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: Ömer Kişi, Mehmet Gürdal
Format: Article
Language:English
Published: 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
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.
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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