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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Main Authors: Mariatul Kiftiah, Yundari Yundari, Suryani Suryani, Nover Lauren
Format: Article
Language:English
Published: Universitas Pattimura 2024-10-01
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.
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publisher Universitas Pattimura
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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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AT yundariyundari acompletiontheoremforcomplexvaluedsmetricspace
AT suryanisuryani acompletiontheoremforcomplexvaluedsmetricspace
AT noverlauren acompletiontheoremforcomplexvaluedsmetricspace
AT mariatulkiftiah completiontheoremforcomplexvaluedsmetricspace
AT yundariyundari completiontheoremforcomplexvaluedsmetricspace
AT suryanisuryani completiontheoremforcomplexvaluedsmetricspace
AT noverlauren completiontheoremforcomplexvaluedsmetricspace