ON THE GENERALIZED IMPLICIT QUASI-VARIATIONAL INEQUALITIES

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.