Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 38752, 12 pages
doi:10.1155/2007/38752
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

Recommended by Yeol-Je Cho

Abstract

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.