Existence of Solutions and Convergence of a Multistep Iterative Algorithm for a System of Variational Inclusions with <inline-formula><graphic file="1687-1812-2007-093678-i1.gif"/></inline-formula>-Accretive Operators

Abstract

We introduce and study a new system of variational inclusions with -accretive operators, which contains variational inequalities, variational inclusions, systems of variational inequalities, and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the -accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multistep iterative algorithm for this system of variational inclusions in real -uniformly smooth Banach spaces. The results in this paper unify, extend, and improve some known results in the literature.