IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i4p327-d219766.html
   My bibliography  Save this article

Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces

Author

Listed:
  • Naeem Saleem

    (Department of Mathematics, University of Management and Technology, C-II Johar Town, Lahore 54000, Pakistan)

  • Mujahid Abbas

    (Department of Mathematics, Government College University, Lahore 54000, Pakistan
    Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa)

  • Manuel De la Sen

    (Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, P.O. Box 644 de Bilbao, Barrio Sarriena, 48940 Leioa (Bizkaia), Spain)

Abstract

The purpose of this paper is to introduce α f -proximal H -contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable results in the literature. We also present some examples to support the results obtained herein.

Suggested Citation

  • Naeem Saleem & Mujahid Abbas & Manuel De la Sen, 2019. "Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces," Mathematics, MDPI, vol. 7(4), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:327-:d:219766
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/4/327/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/4/327/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. N. Shahzad & S. Sadiq Basha & R. Jeyaraj, 2011. "Common Best Proximity Points: Global Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 69-78, January.
    2. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    3. 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.
    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. A. Abkar & M. Gabeleh, 2012. "Global Optimal Solutions of Noncyclic Mappings in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 298-305, May.
    2. Ali Abkar & Narges Moezzifar & Azizollah Azizi, 2016. "Best Proximity Point Theorems in Partially Ordered b -Quasi Metric Spaces," Mathematics, MDPI, vol. 4(4), pages 1-16, November.
    3. Bessem Samet, 2013. "Some Results on Best Proximity Points," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 281-291, October.
    4. S. Sadiq Basha & N. Shahzad & R. Jeyaraj, 2013. "Best proximity point theorems: exposition of a significant non-linear programming problem," Journal of Global Optimization, Springer, vol. 56(4), pages 1699-1705, August.
    5. Moosa Gabeleh, 2013. "Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 615-625, August.
    6. V. Sankar Raj & A. Anthony Eldred, 2014. "A Characterization of Strictly Convex Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 703-710, February.
    7. S. Sadiq Basha, 2014. "Best proximity point theorems: unriddling a special nonlinear programming problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 543-553, July.
    8. Hind Alamri & Nawab Hussain & Ishak Altun, 2023. "Proximity Point Results for Generalized p -Cyclic Reich Contractions: An Application to Solving Integral Equations," Mathematics, MDPI, vol. 11(23), pages 1-25, November.
    9. 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.
    10. Moosa Gabeleh, 2015. "Best Proximity Point Theorems via Proximal Non-self Mappings," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 565-576, February.
    11. Slah Sahmim & Abdelbasset Felhi & Hassen Aydi, 2019. "Convergence and Best Proximity Points for Generalized Contraction Pairs," Mathematics, MDPI, vol. 7(2), pages 1-12, February.
    12. Hussain, Nawab & Kutbi, M.A. & Salimi, Peyman, 2020. "Global optimal solutions for proximal fuzzy contractions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    13. 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.
    14. Victoria Olisama & Johnson Olaleru & Hudson Akewe, 2017. "Best Proximity Point Results for Some Contractive Mappings in Uniform Spaces," International Journal of Analysis, Hindawi, vol. 2017, pages 1-8, April.
    15. Muhammad Zahid & Fahim Ud Din & Mudasir Younis & Haroon Ahmad & Mahpeyker Öztürk, 2024. "Some Results on Multivalued Proximal Contractions with Application to Integral Equation," Mathematics, MDPI, vol. 12(22), pages 1-21, November.
    16. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    17. Binayak S. Choudhury & Nikhilesh Metiya & Pranati Maity, 2014. "Best Proximity Point Results in Complex Valued Metric Spaces," International Journal of Analysis, Hindawi, vol. 2014, pages 1-6, August.

    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:7:y:2019:i:4:p:327-:d:219766. 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.