, Volume 83, Issue 2, pp 391-403

Multi-valued variational inequalities with K-pseudomonotone operators

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In this paper, we first employ the 1961 celebrated Fan lemma to derive a very general existence result for multi-valued variational inequalities involving multi-valued K-pseudomonotone operators. It will be seen that this result improves and unifies existence results of variational inequalities for monotone operators. Next, we establish some uniqueness results for multi-valued variational inequalities by introducing the concepts of strict, α, and strong K-pseudomonotonicity of multi-valued operators, respectively. These uniqueness results appear to be new even if the underlying space is finite-dimensional.

Communicated by S. Schaible
This work was partially supported by the National Science Council Grant NSC 82-0208-M-110-023. The author would like to express his sincere thanks to the referees for their valuable comments and suggestions that improved this paper substantially.