IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p281-d1025982.html
   My bibliography  Save this article

Common Best Proximity Points and Completeness of ℱ−Metric Spaces

Author

Listed:
  • Mi Zhou

    (School of Science and Technology, Sanya University, Sanya 572000, 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 54770, Pakistan)

  • Basit Ali

    (Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan)

  • Misha Mohsin

    (Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan)

  • Antonio Francisco Roldán López de Hierro

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

Abstract

In this paper, we introduce three classes of proximal contractions that are called the proximally λ − ψ − dominated contractions, generalized η β γ − proximal contractions and Berinde-type weak proximal contractions, and obtain common best proximity points for these proximal contractions in the setting of F − metric spaces. Further, we obtain the best proximity point result for generalized α − φ − proximal contractions in F − metric spaces. As an application, fixed point and coincidence point results for these contractions are obtained. Some examples are provided to support the validity of our main results. Moreover, we obtain a completeness characterization of the F − metric spaces via best proximity points.

Suggested Citation

  • Mi Zhou & Naeem Saleem & Basit Ali & Misha Mohsin & Antonio Francisco Roldán López de Hierro, 2023. "Common Best Proximity Points and Completeness of ℱ−Metric Spaces," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:281-:d:1025982
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/281/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/281/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. T. Q. Bao & S. Cobzaş & A. Soubeyran, 2018. "Variational principles, completeness and the existence of traps in behavioral sciences," Annals of Operations Research, Springer, vol. 269(1), pages 53-79, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ştefan Cobzaş, 2024. "The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces," Mathematics, MDPI, vol. 12(3), pages 1-13, February.
    2. L. P. Hai & L. Huerga & P. Q. Khanh & V. Novo, 2019. "Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems," Journal of Global Optimization, Springer, vol. 74(2), pages 361-382, June.
    3. Majid Fakhar & Mohammadreza Khodakhah & Ali Mazyaki & Antoine Soubeyran & Jafar Zafarani, 2022. "Variational rationality, variational principles and the existence of traps in a changing environment," Journal of Global Optimization, Springer, vol. 82(1), pages 161-177, January.
    4. Le Phuoc Hai, 2021. "Ekeland variational principles involving set perturbations in vector equilibrium problems," Journal of Global Optimization, Springer, vol. 79(3), pages 733-756, March.
    5. Le Phuoc Hai & Phan Quoc Khanh & Antoine Soubeyran, 2022. "General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 347-373, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:281-:d:1025982. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.