Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 976505, 23 pages
Research Article

Generalized Systems of Variational Inequalities and Projection Methods for Inverse-Strongly Monotone Mappings

1Department of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, Thailand
2Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand
3Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 20 February 2011; Accepted 3 May 2011

Academic Editor: Jianshe Yu

Copyright © 2011 Wiyada Kumam 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.


We introduce an iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for three inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply to find solutions of a general system of variational inequality and a zero of a maximal monotone operator in a real Hilbert space. As applications, at the end of the paper we utilize our results to study some convergence problem for strictly pseudocontractive mappings. Our results include the previous results as special cases extend and improve the results of Ceng et al., (2008) and many others.