IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2012y2012i1n538912.html

Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed‐Point Problems, and Variational Inclusions with Application to Minimization Problem

Author

Listed:
  • Tanom Chamnarnpan
  • Poom Kumam

Abstract

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for a β‐inverse‐strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.

Suggested Citation

  • Tanom Chamnarnpan & Poom Kumam, 2012. "Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed‐Point Problems, and Variational Inclusions with Application to Minimization Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:538912
    DOI: 10.1155/2012/538912
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/538912
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/538912?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. Thanyarat Jitpeera & Poom Kumam, 2011. "A General Iterative Algorithm for Generalized Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-25, April.
    2. Poom Kumam & Usa Hamphries & Phayap Katchang, 2011. "Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-28, September.
    3. Poom Kumam & Usa Hamphries & Phayap Katchang, 2011. "Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    4. Pongsakorn Sunthrayuth & Poom Kumam, 2011. "A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    5. Pongsakorn Sunthrayuth & Poom Kumam, 2011. "A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-29, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Haitao Che & Xintian Pan, 2013. "A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Haitao Che & Meixia Li & Xintian Pan, 2012. "Convergence Theorems for Equilibrium Problems and Fixed‐Point Problems of an Infinite Family of ki‐Strictly Pseudocontractive Mapping in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

    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. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "An Iterative Method for Solving a System of Mixed Equilibrium Problems, System of Quasivariational Inclusions, and Fixed Point Problems of Nonexpansive Semigroups with Application to Optimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Haitao Che & Meixia Li & Xintian Pan, 2012. "Convergence Theorems for Equilibrium Problems and Fixed‐Point Problems of an Infinite Family of ki‐Strictly Pseudocontractive Mapping in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Bashir Ali & G. C. Ugwunnadi, 2012. "Convergence Theorem for a Family of Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, July.
    4. Haitao Che & Xintian Pan, 2013. "A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Jong Soo Jung, 2012. "Weak Convergence Theorems for Strictly Pseudocontractive Mappings and Generalized Mixed Equilibrium Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Poom Kumam & Phayap Katchang, 2012. "A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Pongsakorn Sunthrayuth & Poom Kumam, 2011. "A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    8. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

    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:538912. 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.