IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v140y2009i2d10.1007_s10957-008-9446-7.html
   My bibliography  Save this article

Solution Existence of Variational Inequalities with Pseudomonotone Operators in the Sense of Brézis

Author

Listed:
  • B. T. Kien

    (Hanoi University of Civil Engineering)

  • M. M. Wong

    (Meiho Institute of Technology)

  • N. C. Wong

    (National Sun Yat-Sen University)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

This paper is concerned with the study of the solution existence of variational inequalities and generalized variational inequalities in reflexive Banach spaces with pseudomonotone operators in the sense of Brézis. The obtained results cover some preceding results in Browder (J. Funct. Anal. 11:251–294, 1972), Brézis (Ann. Inst. Fourier 18:115–175, 1968), Kinderlehrer and Stampacchia (An Introduction to Variational Inequalities and Their Applications, Academic Press, San Diego, 1980), Zeidler (Nonlinear Functional Analysis and Its Applications, II/B, Springer, Berlin, 1990).

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joptap:v:140:y:2009:i:2:d:10.1007_s10957-008-9446-7
    DOI: 10.1007/s10957-008-9446-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-008-9446-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-008-9446-7?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. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    2. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
    3. P. Daniele & A. Maugeri & W. Oettli, 1999. "Time-Dependent Traffic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 543-555, December.
    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. 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.
    2. Daniel Steck, 2019. "Brezis Pseudomonotonicity is Strictly Weaker than Ky–Fan Hemicontinuity," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 318-323, April.
    3. 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.

    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. Ciarcià, Carla & Daniele, Patrizia, 2016. "New existence theorems for quasi-variational inequalities and applications to financial models," European Journal of Operational Research, Elsevier, vol. 251(1), pages 288-299.
    2. Patrizia Daniele & Mariagrazia Lorino & Cristina Mirabella, 2016. "The Financial Equilibrium Problem with a Markowitz-Type Memory Term and Adaptive Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 276-296, October.
    3. Y. Chiang, 2010. "Variational inequalities on weakly compact sets," Journal of Global Optimization, Springer, vol. 46(3), pages 465-473, March.
    4. Mircea Balaj, 2021. "Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization," Mathematische Nachrichten, Wiley Blackwell, vol. 294(7), pages 1262-1276, July.
    5. 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.
    6. John Cotrina & Javier Zúñiga, 2019. "Quasi-equilibrium problems with non-self constraint map," Journal of Global Optimization, Springer, vol. 75(1), pages 177-197, September.
    7. Massimiliano Giuli, 2013. "Closedness of the Solution Map in Quasivariational Inequalities of Ky Fan Type," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 130-144, July.
    8. Somaye Jafari & Ali Farajzadeh & Sirous Moradi, 2016. "Locally Densely Defined Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 804-817, September.
    9. John Cotrina & Anton Svensson, 2021. "The finite intersection property for equilibrium problems," Journal of Global Optimization, Springer, vol. 79(4), pages 941-957, April.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Didier Aussel & Asrifa Sultana & Vellaichamy Vetrivel, 2016. "On the Existence of Projected Solutions of Quasi-Variational Inequalities and Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 818-837, September.
    15. I. Konnov, 2014. "On penalty methods for non monotone equilibrium problems," Journal of Global Optimization, Springer, vol. 59(1), pages 131-138, May.
    16. Annamaria Barbagallo & Stéphane Pia, 2015. "Weighted Quasi-Variational Inequalities in Non-pivot Hilbert Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 781-803, March.
    17. 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.
    18. J. H. Fan & X. G. Wang, 2009. "Solvability of Generalized Variational Inequality Problems for Unbounded Sets in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 59-74, October.
    19. Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2017. "Common Fixed Point Theorems in Topological Vector Spaces via Intersection Theorems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 443-458, May.
    20. I. Konnov & D. Dyabilkin, 2011. "Nonmonotone equilibrium problems: coercivity conditions and weak regularization," Journal of Global Optimization, Springer, vol. 49(4), pages 575-587, April.

    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:joptap:v:140:y:2009:i:2:d:10.1007_s10957-008-9446-7. 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.