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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
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    References listed on IDEAS

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    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. 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.
    3. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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