Generalized nonlinear mixed quasi-variational inequalities

In this paper, we introduce and study a new class of quasi-variational ineq ualities, 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 th is class of generalized nonlinear set-valued mixed quasi-variational inequa lities. We prove the existence of solution for this kind of generalized non linear set-valued mixed quasivariational inequalities without compactness a nd the convergence of iterative sequences generated by the algorithms. We a lso discuss the convergence and stability of perturbed iterative algorithm for solving a class of generalized nonlinear mixed quasi-variational inequa lities. (C) 2000 Elsevier Science Ltd. All rights reserved.