Multivalued variational inequalities and resolvent equations

Abstract

In this paper, we introduce and study some new classes of multivalued variational inequalities. These classes are more general and include the previously known classes of variational inequalities and related optimization problems as special cases. We also introduce some new resolvent equation problems. We prove that multivalued variational inequalities are equivalent to the fixed point problems and the resolvent equations. This equivalence is used to discuss the existence of the solution of the multivalued variational inequalities and suggest iterative algorithms for computing the approximate solutions. The convergence analysis is also studied.