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Multi-valued variational inequalities with K-pseudomonotone operators
Authors:J. C. Yao
Affiliation:(1) Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC
Abstract: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, agr, and strong K-pseudomonotonicity of multi-valued operators, respectively. These uniqueness results appear to be new even if the underlying space is finite-dimensional.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.
Keywords:Multi-valued variational inequalities  K-pseudomonotone operators  strictly K-pseudomonotone operators  strongly K-pseudomonotone operators  upper semicontinuous operators
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