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Existence and iterative approximation of solutions of multi-valued generalized quasi-variational-like inequalities: an auxiliary principle approach. (English) Zbl 1188.49011

Summary: We consider an auxiliary problem for a generalized quasi-variational-like inequality problem involving multi-valued mappings in real Hilbert space and establish an existence and uniqueness result for this auxiliary problem. Using this result, we construct an algorithm for the generalized quasi-variational-like inequality problem. Further, we prove the existence of a solution of a generalized quasi-variational-like inequality problem and discuss convergence criteria of the algorithm.

MSC:

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