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Existence Theorems for Variational Inequalities in Banach Spaces

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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.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, China

    L. C. Zeng (Professor)

  2. Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan

    J. C. Yao (Professor)

Authors
  1. L. C. Zeng
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  2. J. C. Yao
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Corresponding author

Correspondence to J. C. Yao.

Additional information

Communicated by F. Giannessi

L. C. Zeng, His research was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and by the Dawn Program Foundation, Shanghai, China.

J. C. Yao, His research was partially supported by the National Science Council of the Republic of China

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Zeng, L.C., Yao, J.C. Existence Theorems for Variational Inequalities in Banach Spaces. J Optim Theory Appl 132, 321–337 (2007). https://doi.org/10.1007/s10957-006-9139-z

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