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The generalized Wiener-Hopf equation and the approximation methods are used to propose a perturbed iterative method to compute the solutions of a general class of nonlinear variational inequalities.

We provide a sensitivity result for the solutions to the following finite-dimensional quasi-variational inequality $$QVIu\in K\left(u\right),〈C\left(u\right),v-u〉\ge 0,\mathrm{\forall }v\in K\left(u\right),$$ when both the operator $C$ and the convex $K$ are perturbed. In particular, we prove the Hölder continuity of the solution sets of the problems perturbed around the original problem. All the results may be extended to infinite-dimensional (QVI).