On the Generalized Implicit Quasivariational Inequalities

In the present paper, we introduce and study a new class of generalized nonlinear implicit quasivariational inequalities for set-valued mappings and construct some new iterative algorithms. We prove the existence of solutions for this class of generalized nonlinear implicit quasivariational inequalities for set-valued mappings without compactness and the convergence of iterative sequences generated by the algorithms. We also study a new perturbed iterative algorithm for solving a class of general strongly nonlinear quasivariational inequalities.