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Multi-valued variational inequalities with \(K\)-pseudomonotone operators. (English) Zbl 0812.47055
Summary: 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, \(\alpha\), and strong \(K\)-pseudomonotonicity of multi-valued operators, respectively. These uniqueness results appear to be new even if the underlying space is finite-dimensional.

47H05 Monotone operators and generalizations
49J40 Variational inequalities
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