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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: \[ (w- z, v- f(x))\geq 0,\quad \forall v\in K, \] 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.

MSC:

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