Open Access

Existence of Solutions and Convergence of a Multistep Iterative Algorithm for a System of Variational Inclusions with -Accretive Operators

Fixed Point Theory and Applications20072007:093678

DOI: 10.1155/2007/93678

Received: 5 April 2007

Accepted: 6 July 2007

Published: 29 August 2007

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.

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Authors’ Affiliations

(1)
College of Mathematics and Computer Science, Chongqing Normal University
(2)
Department of Management Science, School of Management, Fudan University
(3)
The Institute of Safety Management, Beijing University of Chemical Technology

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© Jian-Wen Peng et al. 2007

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