IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v55y2013i1p27-51.html
   My bibliography  Save this article

Existence theorems for generalized set-valued mixed (quasi-)variational inequalities in Banach spaces

Author

Listed:
  • Lu-Chuan Ceng
  • Jen-Chih Yao

Abstract

In this paper, utilizing the properties of the generalized f -projection operator and the well-known KKM and Kakutani–Fan–Glicksberg theorems, under quite mide assumptions, we derive some new existence theorems for the generalized set-valued mixed variational inequality and the generalized set-valued mixed quasi-variational inequality in reflexive and smooth Banach spaces, respectively. The results presented in this paper can be viewed as the supplement, improvement and extension of recent results in Wu and Huang (Nonlinear Anal 71:2481–2490, 2009 ). Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Lu-Chuan Ceng & Jen-Chih Yao, 2013. "Existence theorems for generalized set-valued mixed (quasi-)variational inequalities in Banach spaces," Journal of Global Optimization, Springer, vol. 55(1), pages 27-51, January.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:1:p:27-51
    DOI: 10.1007/s10898-011-9811-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-011-9811-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-011-9811-1?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    2. L. C. Zeng & J. C. Yao, 2007. "Existence Theorems for Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 321-337, February.
    3. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
    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. L. C. Ceng & A. Petruşel, 2010. "Krasnoselski-Mann Iterations for Hierarchical Fixed Point Problems for a Finite Family of Nonself Mappings in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 617-639, September.
    2. 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.
    3. Rapeepan Kraikaew & Satit Saejung, 2012. "On Maingé’s Approach for Hierarchical Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 71-87, July.
    4. Giuseppe Marino & Hong-Kun Xu, 2011. "Explicit Hierarchical Fixed Point Approach to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 61-78, April.
    5. 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.
    6. 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.
    7. Pham Ngoc Anh, 2023. "New Outer Proximal Methods for Solving Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 479-501, August.
    8. 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.
    9. 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.
    10. B. T. Kien & M. M. Wong & N. C. Wong & J. C. Yao, 2009. "Solution Existence of Variational Inequalities with Pseudomonotone Operators in the Sense of Brézis," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 249-263, February.
    11. Bui Trong Kien & Xiaolong Qin & Ching-Feng Wen & Jen-Chih Yao, 2021. "The Galerkin Method and Regularization for Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 578-596, May.
    12. Y. Chiang & J. C. Yao, 2004. "Vector Variational Inequalities and the (S)+ Condition," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 271-290, November.
    13. N. El Farouq, 2001. "Pseudomonotone Variational Inequalities: Convergence of Proximal Methods," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 311-326, May.
    14. Yonghong Yao & Mihai Postolache, 2012. "Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 273-287, October.
    15. P. E. Maingé, 2008. "New Approach to Solving a System of Variational Inequalities and Hierarchical Problems," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 459-477, September.
    16. Mostafa Ghadampour & Ebrahim Soori & Ravi P. Agarwal & Donal O’Regan, 2022. "A Strong Convergence Theorem for Solving an Equilibrium Problem and a Fixed Point Problem Using the Bregman Distance," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 854-877, December.
    17. L. C. Zeng & J. C. Yao, 2007. "Existence Theorems for Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 321-337, February.
    18. Yonghong Yao & Yeong-Cheng Liou & Shin Kang, 2013. "Two-step projection methods for a system of variational inequality problems in Banach spaces," Journal of Global Optimization, Springer, vol. 55(4), pages 801-811, April.
    19. L. C. Ceng & S. Schaible & J. C. Yao, 2009. "Strong Convergence of Iterative Algorithms for Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 265-283, May.
    20. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, November.

    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:spr:jglopt:v:55:y:2013:i:1:p:27-51. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.