IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n130439.html

On Best Proximity Point Theorems without Ordering

Author

Listed:
  • A. P. Farajzadeh
  • S. Plubtieng
  • K. Ungchittrakool

Abstract

Recently, Basha (2013) addressed a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric. He assumed that if A and B are nonvoid subsets of a partially ordered set that is equipped with a metric and S is a non‐self‐mapping from A to B, then the mapping S has an optimal approximate solution, called a best proximity point of the mapping S, to the operator equation Sx = x, when S is a continuous, proximally monotone, ordered proximal contraction. In this note, we are going to obtain his results by omitting ordering, proximal monotonicity, and ordered proximal contraction on S.

Suggested Citation

  • A. P. Farajzadeh & S. Plubtieng & K. Ungchittrakool, 2014. "On Best Proximity Point Theorems without Ordering," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:130439
    DOI: 10.1155/2014/130439
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/130439
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/130439?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. S. Sadiq Basha, 2011. "Best proximity points: global optimal approximate solutions," Journal of Global Optimization, Springer, vol. 49(1), pages 15-21, January.
    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. S.Sadiq Basha, 2025. "A Generalization of the Contraction Principle to Produce optimal Approximate Solutions," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-12, December.
    2. 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.
    3. 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.
    4. 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.
    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. Bessem Samet, 2013. "Some Results on Best Proximity Points," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 281-291, October.
    7. 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.
    8. Maryam A. Alghamdi & Naseer Shahzad & Francesca Vetro, 2013. "Best Proximity Points for Some Classes of Proximal Contractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    10. 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.
    11. 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.
    12. 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.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2014:y:2014:i:1:n:130439. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.