IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2012y2012i1n516897.html

Strong Convergence of a Hybrid Iteration Scheme for Equilibrium Problems, Variational Inequality Problems and Common Fixed Point Problems, of Quasi‐ϕ‐Asymptotically Nonexpansive Mappings in Banach Spaces

Author

Listed:
  • Jing Zhao

Abstract

We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi‐ϕ‐asymptotically nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality problem for a γ‐inverse strongly monotone mapping in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others.

Suggested Citation

  • Jing Zhao, 2012. "Strong Convergence of a Hybrid Iteration Scheme for Equilibrium Problems, Variational Inequality Problems and Common Fixed Point Problems, of Quasi‐ϕ‐Asymptotically Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:516897
    DOI: 10.1155/2012/516897
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/516897
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/516897?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. Siwaporn Saewan & Poom Kumam & Kriengsak Wattanawitoon, 2010. "Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-25, January.
    2. Siwaporn Saewan & Poom Kumam & Kriengsak Wattanawitoon, 2010. "Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    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. Yekini Shehu, 2010. "A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Kriengsak Wattanawitoon & Poom Kumam, 2012. "A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Siwaporn Saewan & Poom Kumam, 2010. "Modified Hybrid Block Iterative Algorithm for Convex Feasibility Problems and Generalized Equilibrium Problems for Uniformly Quasi‐ϕ‐Asymptotically Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    4. Kriengsak Wattanawitoon & Poom Kumam, 2012. "The Modified Block Iterative Algorithms for Asymptotically Relatively Nonexpansive Mappings and the System of Generalized Mixed Equilibrium Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Yonghong Yao & Yeong-Cheng Liou, 2010. "Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    6. Zi-Ming Wang & Poom Kumam, 2013. "Hybrid Projection Algorithm for Two Countable Families of Hemirelatively Nonexpansive Mappings and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    7. Zhaoli Ma & Lin Wang & Yunhe Zhao, 2012. "Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi‐ϕ‐Asymptotically Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    8. Siwaporn Saewan & Poom Kumam, 2010. "A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi‐Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    9. 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.

    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:jnljam:v:2012:y:2012:i:1:n:516897. 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/4185 .

    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.