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On generalized variational inequalities involving relaxed Lipschitz and relaxed monotone operators. (English) Zbl 0902.49009
The standard projection technique in Hilbert spaces has been used to construct the solution of the problem: Find $x\in H$ with $f(x)\in K$, $w\in S(x)$, $z\in T(x)$ and such that the following generalized variational inequality holds: $$(w- z, v- f(x))\ge 0,\quad \forall v\in K,$$ where $K\subset H$ is a closed convex subset of a Hilbert space $H$, $f: H\to H$ is a given strongly monotone and Lipschitz continuous operator, the multivalued mappings $S, T: H\to 2^H$ are assumed to satisfy the appropriate conditions of relaxed monotonicity and Lipschitz continuity.

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