A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE

  • Mariatul Kiftiah Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Tanjungpura, Indonesia https://orcid.org/0000-0002-6634-2711
  • Yundari Yundari Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Tanjungpura, Indonesia
  • Suryani Suryani Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Tanjungpura, Indonesia
  • Nover Lauren Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Tanjungpura, Indonesia
DOI: https://doi.org/10.30598/barekengvol18iss4pp2747-2756
Keywords: Completion, Complex, S-metric Space

Abstract

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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Published
2024-10-14
How to Cite
[1]
M. Kiftiah, Y. Yundari, S. Suryani, and N. Lauren, “A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE”, BAREKENG: J. Math. & App., vol. 18, no. 4, pp. 2747-2756, Oct. 2024.
Issue
Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2024 Mariatul Kiftiah, Yundari Yundari, Suryani Suryani, Nover Lauren

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