Generalized nonlinear mixed quasi-variational inequalities

In this paper, we introduce and study a new class of quasi-variational inequalities, which is called the generalized nonlinear set-valued mixed quasi-variational inequality. Using the resolvent operator technique for maximal monotone mapping, we construct some new iterative algorithms for solving this class of generalized nonlinear set-valued mixed quasi-variational inequalities. We prove the existence of solution for this kind of generalized nonlinear set-valued mixed quasivariational inequalities without compactness and the convergence of iterative sequences generated by the algorithms. We also discuss the convergence and stability of perturbed iterative algorithm for solving a class of generalized nonlinear mixed quasi-variational inequalities.