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Generalized nonlinear mixed quasi-variational inequalities. (English) Zbl 0960.47036
The problem is studied to find in a Hilbert space $u$, $x\in Su$, $y\in Tu$, and $z\in Gu$ such that the inclusion $0\in N(x,y)+M(p(u),z)$ holds. Here, $M(\cdot,z)$ is assumed to be maximal monotone where the resolvent $(I+\rho M(\cdot,z))^{-1}$ 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.

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