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Existence Theorems for Variational Inequalities in Banach Spaces

Author

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  • L. C. Zeng

    (Shanghai Normal University)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

In this paper, by employing the notion of generalized projection operators and the well-known Fan’s lemma, we establish some existence results for the variational inequality problem and the quasivariational inequality problem in reflexive, strictly convex, and smooth Banach spaces. We propose also an iterative method for approximate solutions of the variational inequality problem and we establish some convergence results for this iterative method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:132:y:2007:i:2:d:10.1007_s10957-006-9139-z
    DOI: 10.1007/s10957-006-9139-z
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    References listed on IDEAS

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    1. 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. 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.
    2. 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.
    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.

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