In the present paper, we introduce and study a new class of generalize
d nonlinear implicit quasivariational inequalities for set-valued mapp
ings and construct some new iterative algorithms. We prove the existen
ce of solutions for this class of generalized nonlinear implicit quasi
variational inequalities for set-valued mappings without compactness a
nd 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. (C) 1997
Academic Press.