IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2012y2012i1n569592.html

Algorithms for Solving System of Extended General Variational Inclusions and Fixed Points Problems

Author

Listed:
  • Narin Petrot
  • Javad Balooee

Abstract

We introduce a new system of extended general nonlinear variational inclusions with different nonlinear operators and establish the equivalence between the aforesaid system and the fixed point problem. By using this equivalent formulation, we prove the existence and uniqueness theorem for solution of the system of extended general nonlinear variational inclusions. We suggest and analyze a new resolvent iterative algorithm to approximate the unique solution of the system of extended general nonlinear variational inclusions which is a fixed point of a nearly uniformly Lipschitzian mapping. Subsequently, the convergence analysis of the proposed iterative algorithm under some suitable conditions is considered. Furthermore, some related works to our main problem are pointed out and discussed.

Suggested Citation

  • Narin Petrot & Javad Balooee, 2012. "Algorithms for Solving System of Extended General Variational Inclusions and Fixed Points Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:569592
    DOI: 10.1155/2012/569592
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/569592
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/569592?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. Javad Balooee & Yeol Je Cho & Mee Kwang Kang, 2012. "Projection Methods and a New System of Extended General Regularized Nonconvex Set-Valued Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, December.
    2. Jittiporn Suwannawit & Narin Petrot, 2012. "Existence and Stability of Iterative Algorithm for a System of Random Set-Valued Variational Inclusion Problems Involving ( ð ´ , ð ‘š , 𠜂 )-Generalized Monotone Operators," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-21, May.
    3. Narin Petrot, 2010. "Some Existence Theorems for Nonconvex Variational Inequalities Problems," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-9, February.
    4. Narin Petrot, 2010. "Some Existence Theorems for Nonconvex Variational Inequalities Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    5. C. E. Chidume & K. R. Kazmi & H. Zegeye, 2004. "Iterative approximation of a solution of a general variational-like inclusion in Banach spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-10, January.
    6. Jittiporn Suwannawit & Narin Petrot, 2012. "Existence and Stability of Iterative Algorithm for a System of Random Set‐Valued Variational Inclusion Problems Involving (A, m, η)‐Generalized Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Javad Balooee & Yeol Je Cho & Mee Kwang Kang, 2012. "Projection Methods and a New System of Extended General Regularized Nonconvex Set‐Valued Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    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. Jittiporn Suwannawit & Narin Petrot, 2013. "Existence Theorems for Quasivariational Inequality Problem on Proximally Smooth Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(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. Yuhuan Chen & Chenfu Yi & Jian Zhong, 2013. "Linear Simultaneous Equations’ Neural Solution and Its Application to Convex Quadratic Programming with Equality‐Constraint," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Shamshad Husain & Sanjeev Gupta & Vishnu Narayan Mishra, 2013. "Generalized -Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions," Journal of Mathematics, Hindawi, vol. 2013, pages 1-10, June.

    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:2012:y:2012:i:1:n:569592. 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.