IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v290y2016icp412-425.html
   My bibliography  Save this article

Error estimates for approximation of coupled best proximity points for cyclic contractive maps

Author

Listed:
  • Ilchev, A.
  • Zlatanov, B.

Abstract

We enrich the known results about coupled fixed and best proximity points of cyclic contraction ordered pair of maps. The uniqueness of the coupled best proximity points for cyclic contraction ordered pair of maps in a uniformly convex Banach space is proven. We find a priori and a posteriori error estimates for the coupled best proximity points, obtained by sequences of successive iterations, when the underlying Banach space has modulus of convexity of power type. A looser conditions are presented for the existence and uniqueness of coupled fixed points of a cyclic contraction ordered pair of maps in a complete metric space and a priori, a posteriori error estimates and the rate of convergence for the coupled fixed points are obtained for the sequences of successive iterations. We apply these results for solving systems of integral equations, systems of linear and nonlinear equations.

Suggested Citation

  • Ilchev, A. & Zlatanov, B., 2016. "Error estimates for approximation of coupled best proximity points for cyclic contractive maps," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 412-425.
  • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:412-425
    DOI: 10.1016/j.amc.2016.06.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316303939
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2016.06.022?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. Miroslav Hristov & Atanas Ilchev & Boyan Zlatanov, 2020. "On the Best Proximity Points for p –Cyclic Summing Contractions," Mathematics, MDPI, vol. 8(7), pages 1-11, July.
    2. Usurelu, Gabriela Ioana & Turcanu, Teodor, 2021. "Best proximity points of (EP)-operators with qualitative analysis and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 215-230.
    3. Yulia Dzhabarova & Stanimir Kabaivanov & Margarita Ruseva & Boyan Zlatanov, 2020. "Existence, Uniqueness and Stability of Market Equilibrium in Oligopoly Markets," Administrative Sciences, MDPI, vol. 10(3), pages 1-32, September.

    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:eee:apmaco:v:290:y:2016:i:c:p:412-425. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.