Resolvent equations technique for general variational inclusions

Abstract

In this paper, we introduce and study a new class of variational inclusions and resolvent equations, respectively, and establish the equivalence between the variational inclusions and the resolvent equations. Using the resolvent equations technique, we construct some new iterative algorithms for solving the classes of varitional inclusions and resolvent equations. Under suitable conditions, the convergence analyses of the iterative algorithms are also studied. Our results include several previously known results as special cases.