IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2012y2012i1n493862.html

Modified Noor′s Extragradient Method for Solving Generalized Variational Inequalities in Banach Spaces

Author

Listed:
  • Shunhou Fan
  • Shin Min Kang
  • Muhammad Aslam Noor
  • Yonghong Yao

Abstract

Motivated and inspired by Korpelevich′s and Noor′s extragradient methods, we suggest an extragradient method by using the sunny nonexpansive retraction which has strong convergence for solving the generalized variational inequalities in Banach spaces.

Suggested Citation

  • Shunhou Fan & Shin Min Kang & Muhammad Aslam Noor & Yonghong Yao, 2012. "Modified Noor′s Extragradient Method for Solving Generalized Variational Inequalities in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:493862
    DOI: 10.1155/2012/493862
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/493862
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/493862?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. Yonghong Yao & Yeong-Cheng Liou & Cun-Lin Li & Hui-To Lin, 2012. "Extended Extragradient Methods for Generalized Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, March.
    3. M. A. Noor & E. A. Al-Said, 1999. "Wiener–Hopf Equations Technique for Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 705-714, December.
    4. Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
    6. Yonghong Yao & Yeong-Cheng Liou & Cun-Lin Li & Hui-To Lin, 2012. "Extended Extragradient Methods for Generalized Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, November.
    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. Yeong-Cheng Liou & Yonghong Yao & Chun-Wei Tseng & Hui-To Lin & Pei-Xia Yang, 2012. "Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Muhammad Aslam Noor & Khalida Inayat Noor, 2012. "Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Muhammad Aslam Noor & Saira Zainab & Yonghong Yao, 2012. "Implicit Methods for Equilibrium Problems on Hadamard Manifolds," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. H. Zegeye & N. Shahzad, 2013. "Extragradient Method for Solutions of Variational Inequality Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Muhammad Aslam Noor & Khalida Inayat Noor, 2012. "Some New Classes of Extended General Mixed Quasi‐Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Yiran He, 2012. "The Tikhonov Regularization Method for Set‐Valued Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Rudong Chen, 2012. "Iterative Schemes for Fixed Point Computation of Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Ting-jian Xiong & Heng-you Lan, 2014. "Iterative Algorithms for New General Systems of Set‐Valued Variational Inclusions Involving (A, η)‐Maximal Relaxed Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    9. Youli Yu & Pei-Xia Yang & Khalida Inayat Noor, 2012. "Projection Algorithms for Variational Inclusions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    10. Muhammad Aslam Noor & Khalida Inayat Noor, 2012. "Explicit Iterative Method for Variational Inequalities on Hadamard Manifolds," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    11. Muhammad Aslam Noor, 2012. "Parametric Extended General Mixed Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    12. Yonghong Yao & Muhammad Aslam Noor & Yeong-Cheng Liou & Shin Min Kang, 2012. "Iterative Algorithms for General Multivalued Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    13. Muhammad Aslam Noor & Khalida Inayat Noor, 2012. "Existence Results for General Mixed Quasivariational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    14. Yeong-Cheng Liou, 2012. "Computing the Fixed Points of Strictly Pseudocontractive Mappings by the Implicit and Explicit Iterations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    15. Vu Thi Huong & Jen-Chih Yao & Nguyen Dong Yen, 2017. "On the Stability and Solution Sensitivity of a Consumer Problem," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 567-589, November.
    16. Lai-Jiu Lin & Zenn-Tsun Yu & Chih-Sheng Chuang, 2013. "Weak and strong convergence theorems for asymptotically pseudo-contraction mappings in the intermediate sense in Hilbert spaces," Journal of Global Optimization, Springer, vol. 56(1), pages 165-183, May.
    17. N. El Farouq, 2001. "Pseudomonotone Variational Inequalities: Convergence of the Auxiliary Problem Method," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 305-322, November.
    18. Xiang-Kai Sun & Hong-Yong Fu & Yi Chai, 2013. "A Note on Scalar‐Valued Gap Functions for Generalized Vector Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    19. Lateef Olakunle Jolaoso & Adeolu Taiwo & Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2020. "A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 744-766, June.
    20. Y. B. Zhao & G. Isac, 2000. "Quasi-P*-Maps, P(τ, α, β)-Maps, Exceptional Family of Elements, and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 213-231, April.

    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:493862. 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.