A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE
Any complex valued S-metric space where each Cauchy sequence converges to a point in this space is said to be complete. However, there are complex valued S-metric spaces that are incomplete but can be completed. A completion of a complex valued S-metric space ( is defined as a complete complex valu...
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Universitas Pattimura
2024-10-01
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| Series: | Barekeng |
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13851 |
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| author | Mariatul Kiftiah Yundari Yundari Suryani Suryani Nover Lauren |
| author_facet | Mariatul Kiftiah Yundari Yundari Suryani Suryani Nover Lauren |
| author_sort | Mariatul Kiftiah |
| collection | DOAJ |
| description | Any complex valued S-metric space where each Cauchy sequence converges to a point in this space is said to be complete. However, there are complex valued S-metric spaces that are incomplete but can be completed. A completion of a complex valued S-metric space ( is defined as a complete complex valued S-metric space with an isometry such that is dense in In this paper, we prove the existence of a completion for a complex valued S-metric space. The completion is constructed using the quotient space of Cauchy sequence equivalence classes within a complex valued S-metric space. This construction ensures that the new space preserves the essential properties of the original S-metric space while being completeness. Furthermore, isometry and denseness are redefined regarding a complex valued S-metric space, generalizing those established in a complex valued metric space. In addition, an example is also presented to illustrate the concept, demonstrating how to find a unique completion of a complex valued S-metric space. |
| format | Article |
| id | doaj-art-61e9fe71ef66415c8f342c79d06d13d8 |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-61e9fe71ef66415c8f342c79d06d13d82025-08-20T04:01:48ZengUniversitas PattimuraBarekeng1978-72272615-30172024-10-011842747275610.30598/barekengvol18iss4pp2747-275613851A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACEMariatul Kiftiah0Yundari Yundari1Suryani Suryani2Nover Lauren3Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Tanjungpura, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Tanjungpura, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Tanjungpura, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Tanjungpura, IndonesiaAny complex valued S-metric space where each Cauchy sequence converges to a point in this space is said to be complete. However, there are complex valued S-metric spaces that are incomplete but can be completed. A completion of a complex valued S-metric space ( is defined as a complete complex valued S-metric space with an isometry such that is dense in In this paper, we prove the existence of a completion for a complex valued S-metric space. The completion is constructed using the quotient space of Cauchy sequence equivalence classes within a complex valued S-metric space. This construction ensures that the new space preserves the essential properties of the original S-metric space while being completeness. Furthermore, isometry and denseness are redefined regarding a complex valued S-metric space, generalizing those established in a complex valued metric space. In addition, an example is also presented to illustrate the concept, demonstrating how to find a unique completion of a complex valued S-metric space.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13851completioncomplexs-metric space |
| spellingShingle | Mariatul Kiftiah Yundari Yundari Suryani Suryani Nover Lauren A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE Barekeng completion complex s-metric space |
| title | A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE |
| title_full | A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE |
| title_fullStr | A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE |
| title_full_unstemmed | A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE |
| title_short | A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE |
| title_sort | completion theorem for complex valued s metric space |
| topic | completion complex s-metric space |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13851 |
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