Multi-valued variational inequalities with K-pseudomonotone operators |
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Authors: | J. C. Yao |
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Affiliation: | (1) Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC |
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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, , 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. |
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Keywords: | Multi-valued variational inequalities K-pseudomonotone operators strictly K-pseudomonotone operators strongly K-pseudomonotone operators upper semicontinuous operators |
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