49J40,47H06

In this paper, we introduce and study a new class of generalized strongly nonlinear implicit quasivariational inequalities for set-valued mappings and construct some new iterative algorithms for this kind of generalized strongly nonlinear implicit quasivariational inequalities by using the projection method and Nadler's theorem. We prove some existence theorems of solutions for this kind of generalized nonlinear strongly implicit quasivariational inequalities for set-valued mappings without compactness and convergence theorems of iterative sequences generated by the algorithms. ;