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Journal of Optimization Theory and Applications

, Volume 132, Issue 2, pp 321–337 | Cite as

Existence Theorems for Variational Inequalities in Banach Spaces

  • L. C. Zeng
  • J. C. Yao
Article

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.

Keywords

Variational inequalities generalized projection operators KKM theorem fixed points Banach spaces 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina
  2. 2.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungTaiwan

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