IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v164y2015i2d10.1007_s10957-014-0583-x.html
   My bibliography  Save this article

Pythagorean Property and Best-Proximity Point Theorems

Author

Listed:
  • Rafael Espínola

    (IMUS, Universidad de Sevilla)

  • G. Sankara Raju Kosuru

    (Indian Statistical Institute Bangalore)

  • P. Veeramani

    (Indian Institute of Technology Madras)

Abstract

In this paper, a notion called proximally complete pair of subsets of a metric space is introduced, which weakens earlier notions in the theory of best-proximity points. By means of this notion, existence and convergence results of best-proximity points are proven for cyclic contraction mappings, which extent other recent results. By observing geometrical properties of Hilbert spaces, the so-called Pythagorean property is introduced. This property is employed to provide sufficient conditions for a cyclic map to be a cyclic contraction.

Suggested Citation

  • Rafael Espínola & G. Sankara Raju Kosuru & P. Veeramani, 2015. "Pythagorean Property and Best-Proximity Point Theorems," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 534-550, February.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0583-x
    DOI: 10.1007/s10957-014-0583-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-014-0583-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-014-0583-x?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hakan Sahin, 2022. "A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    2. 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.
    3. Poom Kumam & Chirasak Mongkolkeha, 2019. "Global Optimization for Quasi-Noncyclic Relatively Nonexpansive Mappings with Application to Analytic Complex Functions," Mathematics, MDPI, vol. 7(1), pages 1-8, January.

    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:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0583-x. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.