## 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 $$E$$.

### MSC:

 49J40 Variational inequalities 47J20 Variational and other types of inequalities involving nonlinear operators (general)
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### References:

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