Abstract
In this paper, we derive an existence result for generalized variational inequalities associated with multivalued mappings on weakly compact sets under a continuity assumption which is much weaker than the regular complete continuity. As an application, we prove the existence of exceptional families of elements for such mappings on closed convex cones in reflexive Banach spaces when the corresponding complementarity problems have no solutions.
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This work was partially supported by grants from the National Science Council of the Republic of China.
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Chiang, Y. Variational inequalities on weakly compact sets. J Glob Optim 46, 465–473 (2010). https://doi.org/10.1007/s10898-009-9449-4
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DOI: https://doi.org/10.1007/s10898-009-9449-4