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Three-step iterative algorithms for multivalued quasi variational inclusions. (English) Zbl 0986.49006

Let \(H\) be a Hilbert space, \(T\) and \(V\) two set-valued mappings with compact values, \(g\) a single-valued mapping from \(H\) to \(H\), and \(N:H\times H\to H\) a nonlinear mapping. Suppose that \(A:H\times H\) is a maximal monotone mapping with respect to the first argument. In this paper, the author considers the problem of finding \(u\in H\), \(w\in Tu\) and \(y\in V(u)\) such that \[ 0\in M(w,y)+A(g(u),u). \]
By using the resolvent technique and Nadler’s result, the author suggests some iterative algorithms and proves a convergence result.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47H04 Set-valued operators
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