STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE
In this paper, we study some basic properties of bicomplex numbers. We introduce two different types of partial order relations on bicomplex numbers, discuss bicomplex valued metric spaces with respect to two different partial orders, and compare them. We also define a hyperbolic valued metric space...
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| 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
2023-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/534 |
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| _version_ | 1850093884231647232 |
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| author | Subhajit Bera Binod Chandra Tripathy |
| author_facet | Subhajit Bera Binod Chandra Tripathy |
| author_sort | Subhajit Bera |
| collection | DOAJ |
| description | In this paper, we study some basic properties of bicomplex numbers. We introduce two different types of partial order relations on bicomplex numbers, discuss bicomplex valued metric spaces with respect to two different partial orders, and compare them. We also define a hyperbolic valued metric space, the density of natural numbers, the statistical convergence, and the statistical Cauchy property of a sequence of bicomplex numbers and investigate some properties in a bicomplex metric space and prove that a bicomplex metric space is complete if and only if two complex metric spaces are complete. |
| format | Article |
| id | doaj-art-0a5641ddea734acfa8bac17f8aa14700 |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2023-07-01 |
| 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-0a5641ddea734acfa8bac17f8aa147002025-08-20T02:41:48ZengUral 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 Journal2414-39522023-07-019110.15826/umj.2023.1.004176STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACESubhajit Bera0Binod Chandra Tripathy1Tripura University, Suryamaninagar-799022, AgartalaTripura University, Suryamaninagar-799022, AgartalaIn this paper, we study some basic properties of bicomplex numbers. We introduce two different types of partial order relations on bicomplex numbers, discuss bicomplex valued metric spaces with respect to two different partial orders, and compare them. We also define a hyperbolic valued metric space, the density of natural numbers, the statistical convergence, and the statistical Cauchy property of a sequence of bicomplex numbers and investigate some properties in a bicomplex metric space and prove that a bicomplex metric space is complete if and only if two complex metric spaces are complete.https://umjuran.ru/index.php/umj/article/view/534partial order, bi-complex valued metric space, statistically convergent |
| spellingShingle | Subhajit Bera Binod Chandra Tripathy STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE Ural Mathematical Journal partial order, bi-complex valued metric space, statistically convergent |
| title | STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE |
| title_full | STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE |
| title_fullStr | STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE |
| title_full_unstemmed | STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE |
| title_short | STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE |
| title_sort | statistical convergence in a bicomplex valued metric space |
| topic | partial order, bi-complex valued metric space, statistically convergent |
| url | https://umjuran.ru/index.php/umj/article/view/534 |
| work_keys_str_mv | AT subhajitbera statisticalconvergenceinabicomplexvaluedmetricspace AT binodchandratripathy statisticalconvergenceinabicomplexvaluedmetricspace |