TAUBERIAN THEOREM FOR GENERAL MATRIX SUMMABILITY METHOD
In this paper, we prove certain Littlewood–Tauberian theorems for general matrix summability method by imposing the Tauberian conditions such as slow oscillation of usual as well as matrix generated sequence, and the De la Vallée Poussin means of real sequences. Moreover, we demonstrate \((\bar{N},p...
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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
2024-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/708 |
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| author | Bidu Bhusan Jena Priyadarsini Parida Susanta Kumar Paikray |
| author_facet | Bidu Bhusan Jena Priyadarsini Parida Susanta Kumar Paikray |
| author_sort | Bidu Bhusan Jena |
| collection | DOAJ |
| description | In this paper, we prove certain Littlewood–Tauberian theorems for general matrix summability method by imposing the Tauberian conditions such as slow oscillation of usual as well as matrix generated sequence, and the De la Vallée Poussin means of real sequences. Moreover, we demonstrate \((\bar{N},p_{n})\) and \((C,1)\) – summability methods as the generalizations of our proposed general matrix method and establish an equivalence relation connecting them. Finally, we draw several remarks in view of the generalizations of some existing well-known results based on our results. |
| format | Article |
| id | doaj-art-b151ff3ba7a64bd9a0a01f5d38a55b3d |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2024-12-01 |
| 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-b151ff3ba7a64bd9a0a01f5d38a55b3d2025-08-20T03:38:39ZengUral 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 Journal2414-39522024-12-0110210.15826/umj.2024.2.008222TAUBERIAN THEOREM FOR GENERAL MATRIX SUMMABILITY METHODBidu Bhusan Jena0Priyadarsini Parida1Susanta Kumar Paikray2Faculty of Science (Mathematics), Sri Sri University, Cuttack 754006, OdishaDepartment of Mathematics, Kuntala Kumari Sabat Women’s College, Balasore 756003, OdishaDepartment of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, OdishaIn this paper, we prove certain Littlewood–Tauberian theorems for general matrix summability method by imposing the Tauberian conditions such as slow oscillation of usual as well as matrix generated sequence, and the De la Vallée Poussin means of real sequences. Moreover, we demonstrate \((\bar{N},p_{n})\) and \((C,1)\) – summability methods as the generalizations of our proposed general matrix method and establish an equivalence relation connecting them. Finally, we draw several remarks in view of the generalizations of some existing well-known results based on our results.https://umjuran.ru/index.php/umj/article/view/708matrix summability, weighted mean, cesàro mean, slow oscillation, tauberian theorem |
| spellingShingle | Bidu Bhusan Jena Priyadarsini Parida Susanta Kumar Paikray TAUBERIAN THEOREM FOR GENERAL MATRIX SUMMABILITY METHOD Ural Mathematical Journal matrix summability, weighted mean, cesàro mean, slow oscillation, tauberian theorem |
| title | TAUBERIAN THEOREM FOR GENERAL MATRIX SUMMABILITY METHOD |
| title_full | TAUBERIAN THEOREM FOR GENERAL MATRIX SUMMABILITY METHOD |
| title_fullStr | TAUBERIAN THEOREM FOR GENERAL MATRIX SUMMABILITY METHOD |
| title_full_unstemmed | TAUBERIAN THEOREM FOR GENERAL MATRIX SUMMABILITY METHOD |
| title_short | TAUBERIAN THEOREM FOR GENERAL MATRIX SUMMABILITY METHOD |
| title_sort | tauberian theorem for general matrix summability method |
| topic | matrix summability, weighted mean, cesàro mean, slow oscillation, tauberian theorem |
| url | https://umjuran.ru/index.php/umj/article/view/708 |
| work_keys_str_mv | AT bidubhusanjena tauberiantheoremforgeneralmatrixsummabilitymethod AT priyadarsiniparida tauberiantheoremforgeneralmatrixsummabilitymethod AT susantakumarpaikray tauberiantheoremforgeneralmatrixsummabilitymethod |