IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2011y2011i1n632857.html

A Halpern‐Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems

Author

Listed:
  • Utith Inprasit
  • Weerayuth Nilsrakoo

Abstract

A new modified Halpern‐Mann type iterative method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of a relatively nonexpansive mapping and the set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. The results presented in this work improve on the corresponding ones announced by many others.

Suggested Citation

  • Utith Inprasit & Weerayuth Nilsrakoo, 2011. "A Halpern‐Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:632857
    DOI: 10.1155/2011/632857
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2011/632857
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/632857?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. Jian-Wen Peng & Soon-Yi Wu & Jen-Chih Yao, 2010. "A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed‐Point Problems, and Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Prasit Cholamjiak & Suthep Suantai, 2010. "Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-17, September.
    3. 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, Hindawi, vol. 2010, pages 1-24, January.
    4. 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).
    5. Prasit Cholamjiak & Suthep Suantai, 2010. "Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi‐Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    6. Fumiaki Kohsaka & Wataru Takahashi, 2004. "Strong convergence of an iterative sequence for maximal monotone operators in a Banach space," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-11, January.
    7. Jian-Wen Peng & Soon-Yi Wu & Jen-Chih Yao, 2010. "A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed-Point Problems, and Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-27, August.
    8. Fumiaki Kohsaka & Wataru Takahashi, 2004. "Strong convergence of an iterative sequence for maximal monotone operators in a Banach space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2004(3), pages 239-249.
    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. Siwaporn Saewan & Poom Kumam, 2011. "Strong Convergence Theorems for Countable Families of Uniformly Quasi‐ϕ‐Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Prasit Cholamjiak & Suthep Suantai & Yeol Je Cho, 2012. "Strong Convergence to Solutions of Generalized Mixed Equilibrium Problems with Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. 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).
    4. Chaichana Jaiboon & Poom Kumam, 2012. "Viscosity Approximation Method for System of Variational Inclusions Problems and Fixed‐Point Problems of a Countable Family of Nonexpansive Mappings," 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. Kamonrat Nammanee & Suthep Suantai & Prasit Cholamjiak, 2012. "Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. 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).
    8. Yaqin Wang, 2012. "A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    9. Kasamsuk Ungchittrakool, 2013. "Existence and Convergence Theorems by an Iterative Shrinking Projection Method of a Strict Pseudocontraction in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    10. Chakkrid Klin-eam & Suthep Suantai & Wataru Takahashi, 2009. "Strong Convergence of Generalized Projection Algorithms for Nonlinear Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    11. Somyot Plubtieng & Wanna Sriprad, 2009. "Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    12. Pongrus Phuangphoo & Poom Kumam, 2013. "A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi‐ϕ‐Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    13. Jingling Zhang & Yongfu Su & Qingqing Cheng, 2012. "Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    14. Rattanaporn Wangkeeree & Uthai Kamraksa & Rabian Wangkeeree, 2011. "A General Composite Algorithms for Solving General Equilibrium Problems and Fixed Point Problems in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    15. Mathew O. Aibinu & Surendra C. Thakur & Sibusiso Moyo, 2020. "Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    16. S. Saewan & P. Kumam, 2013. "A generalized f-projection method for countable families of weak relatively nonexpansive mappings and the system of generalized Ky Fan inequalities," Journal of Global Optimization, Springer, vol. 56(2), pages 623-645, June.
    17. Ali Abkar & Elahe Shahrosvand & Azizollah Azizi, 2017. "The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces," Mathematics, MDPI, vol. 5(1), pages 1-18, February.
    18. Prasit Cholamjiak & Suthep Suantai, 2013. "Iterative methods for solving equilibrium problems, variational inequalities and fixed points of nonexpansive semigroups," Journal of Global Optimization, Springer, vol. 57(4), pages 1277-1297, 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:jnlaaa:v:2011:y:2011:i:1:n:632857. 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.