The generalized set-valued strongly nonlinear implicit variational inequalities

In this paper, we introduce and study a new class of generalized set-valued strongly nonlinear implicit variational inequalities in Hilbert spaces. We construct the algorithm for solving this kind of generalized set-valued st rongly nonlinear implicit variational inequality problem by using the auxil iary principle technique of Glowinski, Lions, and Tremolieres, prove the ex istence of solutions for this class of generalized set-valued strongly nonl inear implicit variational inequalities and the convergence of iterative se quences generated by the algorithm. (C) 1999 Elsevier Science Ltd. All righ ts reserved.