Abstract
This paper introduces the notion of k-fuzzy metric spaces, which generalizes and extends the concept of fuzzy metric spaces due to George and Veeramani in [A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399.] for the fuzzy sets involving more than one (k) parameters. It is shown that the topology generated by the k-fuzzy metric is first countable, and the k-fuzzy metric space is Hausdorff. Finally, we prove a fixed point theorem, which generalizes and extends the results of Grabiec [M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389.] into k-fuzzy metric spaces.
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References
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We would like to thank the referee for his/her great efforts in proofreading the manuscript.
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This work was supported by the Thailand Science Research and Innovation Fundamental Fund fiscal year 2023 (TUFF 20/2566). Dhananjay Gopal and Abhay S. Ranadive thank the Department of Science and Technology, New Delhi, India, for approving the proposal under the FIST Program scheme (Ref. No. SR/FST/MS/2022/122 dated 19/12/2022).
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DG, AR and SS conceived of the presented idea. WS developed theorems and the proof. All the authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.
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Gopal, D., Sintunavarat, W., Ranadive, A.S. et al. The investigation of k-fuzzy metric spaces with the first contraction principle in such spaces. Soft Comput 27, 11081–11089 (2023). https://doi.org/10.1007/s00500-023-07946-y
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DOI: https://doi.org/10.1007/s00500-023-07946-y