Journal of Applied Mathematics
Volume 2011 (2011), Article ID 164978, 17 pages
http://dx.doi.org/10.1155/2011/164978
Research Article

Strong Convergence Algorithms for Hierarchical Fixed Points Problems and Variational Inequalities

Gendai Gu,1 Shenghua Wang,1,2 and Yeol Je Cho3

1School of Applied Mathematics and Physics, North China Electric Power University, Baoding 071003, China
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
3Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 26 April 2011; Revised 15 June 2011; Accepted 11 July 2011

Academic Editor: Ya Ping Fang

Copyright © 2011 Gendai Gu 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.

Abstract

We introduce a new iterative scheme that converges strongly to a common fixed point of a countable family of nonexpansive mappings in a Hilbert space such that the common fixed point is a solution of a hierarchical fixed point problem. Our results extend the ones of Moudafi, Xu, Cianciaruso et al., and Yao et al.