Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 93678, 20 pages
doi:10.1155/2007/93678

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

Jian-Wen Peng1 , Dao-Li Zhu2 and Xiao-Ping Zheng3

1College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
 2Department of Management Science, School of Management, Fudan University, Shanghai 200433, China
 3The Institute of Safety Management, Beijing University of Chemical Technology, Beijing 100029, China

Abstract

We introduce and study a new system of variational inclusions with (H,η)-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 (H,η)-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 q-uniformly smooth Banach spaces. The results in this paper unify, extend, and improve some known results in the literature.