Research Article Existence of Solutions and Convergence of a Multistep Iterative Algorithm for a System of Variational Inclusions with (H,η)-Accretive Operators

We introduce and study a new system of variational inclusions with (H,η)-accretive op-erators, which contains variational inequalities, variational inclusions, systems of varia-tional inequalities, and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (H,η)-accretive operators, we prove the exis-tence and uniqueness of solution and the convergence of a new multistep iterative algo-rithm for this system of variational inclusions in real q-uniformly smooth Banach spaces. The results in this paper unify, extend, and improve some known results in the litera-ture. Copyright © 2007 Jian-Wen Peng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1