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Best Proximity Point Theorems without Fuzzy P -Property for Several ( ψ − ϕ )-Weak Contractions in Non-Archimedean Fuzzy Metric Spaces

Author

Listed:
  • Mi Zhou

    (School of Science and Technology, University of Sanya, Sanya 572022, China
    Center for Mathematical Research, University of Sanya, Sanya 572022, China
    Academician Guoliang Chen Team Innovation Center, University of Sanya, Sanya 572022, China
    Academician Chunming Rong Workstation, University of Sanya, Sanya 572022, China)

  • Naeem Saleem

    (Department of Mathematics, University of Management and Technology, Lahore 54700, Pakistan)

  • Antonio Francisco Roldán López de Hierro

    (Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain)

  • Xiaolan Liu

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
    South Sichuan Center for Applied Mathematics, Zigong 643000, China)

Abstract

This paper addresses a problem of global optimization in a non-Archimedean fuzzy metric space context without fuzzy P -property. Specifically, it concerns the determination of the fuzzy distance between two subsets of a non-Archimedean fuzzy metric space. Our approach to solving this problem is to find an optimal approximate solution to a fixed point equation. This approach has been well studied within a category of problems called proximity point problems. We explore some new types of ( ψ − ϕ ) -weak proximal contractions and investigate the existence of the unique best proximity point for such kinds of mappings. Subsequently, some fixed point results for corresponding contractions are proved, and some illustrative examples are presented to support the validity of the main results. Moreover, an interesting application in computer science, particularly in the domain of words has been provided. Our work is a fuzzy generalization of the proximity point problem by means of fuzzy fixed point method.

Suggested Citation

  • Mi Zhou & Naeem Saleem & Antonio Francisco Roldán López de Hierro & Xiaolan Liu, 2022. "Best Proximity Point Theorems without Fuzzy P -Property for Several ( ψ − ϕ )-Weak Contractions in Non-Archimedean Fuzzy Metric Spaces," Mathematics, MDPI, vol. 10(21), pages 1-27, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4031-:d:957973
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    References listed on IDEAS

    as
    1. Calogero Vetro & Peyman Salimi, 2013. "Best proximity point results in non-Archimedean fuzzy metric spaces," Fuzzy Information and Engineering, Springer, vol. 5(4), pages 417-429, December.
    2. Manuel De la Sen & Mujahid Abbas & Naeem Saleem, 2017. "On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces," Mathematics, MDPI, vol. 5(2), pages 1-20, April.
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