STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS
In this paper, we extend statistical bounded sequences of real or complex numbers to the setting of sequences of bi-complex numbers. We define the statistical bounded sequence space of bicomplex numbers b^* ∞and also define the statistical bounded sequence spaces of ideals I^1 ∞ and I^2 ∞ . We pro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2023-06-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=13090&lang=ru |
| _version_ | 1797633362711543808 |
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| author | S. Bera B. Ch. Tripathy |
| author_facet | S. Bera B. Ch. Tripathy |
| author_sort | S. Bera |
| collection | DOAJ |
| description | In this paper, we extend statistical bounded sequences
of real or complex numbers to the setting of sequences of bi-complex
numbers. We define the statistical bounded sequence space of bicomplex numbers b^* ∞and also define the statistical bounded sequence spaces of ideals I^1 ∞ and I^2 ∞ . We prove some inclusion relations and provide examples. We establish that b^* ∞ is the direct sum of I^1 ∞ and I^2 ∞ . Also, we prove the decomposition theorem for statistical bounded sequences of bi-complex numbers. Finally, summability properties in the light of J.A. Fridy’s work are studied.
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| first_indexed | 2024-03-11T11:53:04Z |
| format | Article |
| id | doaj.art-aec4ed0788924b889efaad2f7d3907fb |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-03-11T11:53:04Z |
| publishDate | 2023-06-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-aec4ed0788924b889efaad2f7d3907fb2023-11-08T23:59:50ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322023-06-0112 (30)231610.15393/j3.art.2023.13090STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERSS. Bera0B. Ch. Tripathy1Department of Mathematics, Tripura University Suryamaninagar, Agartala-799022, Tripura(W), IndiaDepartment of Mathematics, Tripura University Suryamaninagar, Agartala-799022, Tripura(W), IndiaIn this paper, we extend statistical bounded sequences of real or complex numbers to the setting of sequences of bi-complex numbers. We define the statistical bounded sequence space of bicomplex numbers b^* ∞and also define the statistical bounded sequence spaces of ideals I^1 ∞ and I^2 ∞ . We prove some inclusion relations and provide examples. We establish that b^* ∞ is the direct sum of I^1 ∞ and I^2 ∞ . Also, we prove the decomposition theorem for statistical bounded sequences of bi-complex numbers. Finally, summability properties in the light of J.A. Fridy’s work are studied. https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=13090&lang=runatural densitybi-complexstatistical boundednorm |
| spellingShingle | S. Bera B. Ch. Tripathy STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS Проблемы анализа natural density bi-complex statistical bounded norm |
| title | STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS |
| title_full | STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS |
| title_fullStr | STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS |
| title_full_unstemmed | STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS |
| title_short | STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS |
| title_sort | statistical bounded sequences of bi complex numbers |
| topic | natural density bi-complex statistical bounded norm |
| url | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=13090&lang=ru |
| work_keys_str_mv | AT sbera statisticalboundedsequencesofbicomplexnumbers AT bchtripathy statisticalboundedsequencesofbicomplexnumbers |