Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 38752, 12 pages
Research Article

An Extragradient Method for Fixed Point Problems and Variational Inequality Problems

Yonghong Yao,1 Yeong-Cheng Liou,2 and Jen-Chih Yao3

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Information Management, Cheng Shiu University, Niaosong Township, Kaohsiung 833, Taiwan
3Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan

Received 11 September 2006; Accepted 10 December 2006

Academic Editor: Yeol-Je Cho

Copyright © 2007 Yonghong Yao 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 present an extragradient method for fixed point problems and variational inequality problems. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for monotone mapping.