IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v57y2013i4p1299-1318.html
   My bibliography  Save this article

Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems

Author

Listed:
  • Siwaporn Saewan
  • Poom Kumam
  • Yeol Cho

Abstract

In this paper, we introduce a new hybrid iterative scheme for finding a common element of the set of zeroes of a maximal monotone operator, the set of fixed points of a relatively quasi-nonexpansive mapping, the sets of solutions of an equilibrium problem and the variational inequality problem in Banach spaces. As applications, we apply our results to obtain strong convergence theorems for a maximal monotone operator and quasi-nonexpansive mappings in Hilbert spaces and we consider a problem of finding a minimizer of a convex function. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Siwaporn Saewan & Poom Kumam & Yeol Cho, 2013. "Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1299-1318, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1299-1318
    DOI: 10.1007/s10898-012-0030-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-0030-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-0030-1?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.

    References listed on IDEAS

    as
    1. Xiaolong Qin & Shin Kang & Yeol Cho, 2010. "Approximating zeros of monotone operators by proximal point algorithms," Journal of Global Optimization, Springer, vol. 46(1), pages 75-87, January.
    2. Ying Liu, 2010. "Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings," Journal of Global Optimization, Springer, vol. 46(3), pages 319-329, March.
    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. Lan, Heng-you, 2021. "Approximation-solvability of population biology systems based on p-Laplacian elliptic inequalities with demicontinuous strongly pseudo-contractive operators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Ali Abkar & Moosa Gabeleh, 2013. "Best proximity points of non-self mappings," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 287-295, July.

    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:jglopt:v:57:y:2013:i:4:p:1299-1318. 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: 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.