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On generalized variational inequalities

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Abstract

We obtain a new version of the minimax inequality of Ky Fan. As an application, an existence result for the generalized variational inequality problem with set-valued mappings defined on noncompact sets in Hausdorff topological vector spaces is given. Also, some existence results for the generalized variational inequality problem for quasimonotone and pseudomonotone mappings are obtained.

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Authors and Affiliations

  1. Department of Mathematics, University of Isfahan, Isfahan, 81745-163, Iran

    M. Fakhar

  2. Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran

    M. Fakhar

  3. Sheikhbahaee University and University of Isfahan, Isfahan, 81745-163, Iran

    J. Zafarani

Authors
  1. M. Fakhar
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  2. J. Zafarani
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Correspondence to M. Fakhar.

Additional information

Dedicated to the memory of T. Rapcsák.

The first author was partially supported by a grant from IPM (No. 86470016).

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Fakhar, M., Zafarani, J. On generalized variational inequalities. J Glob Optim 43, 503–511 (2009). https://doi.org/10.1007/s10898-008-9346-2

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  • DOI: https://doi.org/10.1007/s10898-008-9346-2

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