EXPLICIT ITERATIVE METHODS FOR MAXIMAL MONOTONE OPERATORS IN HILBERT SPACES

Abstract

In this paper, we introduce new explicit iterative methods for solving a variational inequality problem over the set of zeros for a maximal monotone operator in Hilbert spaces. By using two resolvents of the monotone operator at each iterate, we prove strong convergence of the methods under a general condition on resolvent parameter. As special cases, new contraction and generalized proximal point methods are obtained. An example is given for illustration and comparison.