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On generalized variational-like inequalities with generalized monotone multivalued mappings. (English) Zbl 1158.49010
Summary: Let $E$ be a reflexive Banach space with the dual space $E^{*}$ and $K$ be a nonempty closed convex subset of $E$. Let us have $\varPsi :K\times K\times E^{*}\rightarrow R$ and $A:E^{*}\rightarrow E^{*}$. We introduce the class of generalized $\alpha $-monotone multifunctions $T:K\rightarrow 2^{E^{*}}$ with respect to $\varPsi $ and $A$ where $\alpha :E\times E\rightarrow R$. By using the KKM technique and the concept of the Hausdorff metric, we establish some existence results for generalized variational-like inequalities with generalized monotone multivalued mappings in $E$.

49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
Full Text: DOI
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