Journal of Applied Mathematics
Volume 2012 (2012), Article ID 560248, 15 pages
http://dx.doi.org/10.1155/2012/560248
Research Article

System of Nonlinear Set-Valued Variational Inclusions Involving a Finite Family of 𝐻 ( ⋅ , ⋅ ) -Accretive Operators in Banach Spaces

Prapairat Junlouchai and Somyot Plubtieng

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 15 February 2012; Accepted 27 March 2012

Academic Editor: Giuseppe Marino

Copyright © 2012 Prapairat Junlouchai and Somyot Plubtieng. 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.

Abstract

We study a new system of nonlinear set-valued variational inclusions involving a finite family of 𝐻 ( ⋅ , ⋅ ) -accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family of 𝐻 ( ⋅ , ⋅ ) -accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variational inclusions. Moreover, we introduce a new iterative scheme and prove a strong convergence theorem for finding solutions for this system.