Algorithm for generalized multivalued variational inequalities in hilbert spaces

AbstractWe introduce a new class of generalized multivalued variational inequality problems (1.1) which contain several existing variational inequality problems as special cases. An iterative algorithm for finding approximate solutions of problem (1.1) is considered. Several convergence results for this algorithm are derived and in particular several existence results of problems (1.1) are obtained. We also introduce a new class of generalized multivalued complementarity problems (5.1) which also contain several known complementarity problems as special cases. It is shown that problem (5.1) is equivalent to problem (1.1) of special type from which several existence results of problem (5.1) are obtained