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Generalized nonlinear mixed quasi-variational inequalities. (English) Zbl 0960.47036

The problem is studied to find in a Hilbert space u, xSu, yTu, and zGu such that the inclusion 0N(x,y)+M(p(u),z) holds. Here, M(·,z) is assumed to be maximal monotone where the resolvent (I+ρM(·,z)) -1 is Lipschitz with respect to z; S,T,G are Lipschitz with respect to the Hausdorff distance, and for p and N Lipschitz and monotonicity conditions are assumed (always with appropriate constants).

An iterative algorithm is suggested whose convergence to a solution is proved. Moreover, for single-valued S,T and G=I also stability of a perturbed algorithm is proved.

47J20Inequalities involving nonlinear operators
47J25Iterative procedures (nonlinear operator equations)
47H05Monotone operators (with respect to duality) and generalizations
49J40Variational methods including variational inequalities