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Monotone generalized variational inequalities and generalized complementarity problems

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Abstract

Some existence results for generalized variational inequalities and generalized complementarity problems involving quasimonotone and pseudomonotone set-valued mappings in reflexive Banach spaces are proved. In particular, some known results for nonlinear variational inequalities and complementarity problems in finite-dimensional and infinite-dimensional Hilbert spaces are generalized to quasimonotone and pseudomonotone set-valued mappings and reflexive Banach spaces. Application to a class of generalized nonlinear complementarity problems studied as mathematical models for mechanical problems is given.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan, P. R. China

    X. P. Ding (Professor)

  2. Department of Mathematics, University of Queensland, St. Lucia, Brisbane, Australia

    E. Tarafdar (Reader)

Authors
  1. X. P. Ding
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  2. E. Tarafdar
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Additional information

Communicated by F. Giannessi

The research of the first author was supported by the National Natural Science Foundation of P. R. China and by the Ethel Raybould Fellowship, University of Queensland, St. Lucia, Brisbane, Australia.

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Ding, X.P., Tarafdar, E. Monotone generalized variational inequalities and generalized complementarity problems. J Optim Theory Appl 88, 107–122 (1996). https://doi.org/10.1007/BF02192024

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