Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 852030, 12 pages
doi:10.1155/2010/852030
Research Article

Two New Iterative Methods for a Countable Family of Nonexpansive Mappings in Hilbert Spaces

Shuang Wang1 and Changsong Hu2

1School of Mathematical Sciences, Yancheng Teachers University, Yancheng, Jiangsu 224051, China
2Department of Mathematics, Hubei Normal University, Huangshi 435002, China

Received 6 August 2010; Accepted 5 October 2010

Academic Editor: Tomonari Suzuki

Copyright © 2010 Shuang Wang and Changsong Hu. 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 consider two new iterative methods for a countable family of nonexpansive mappings in Hilbert spaces. We proved that the proposed algorithms strongly converge to a common fixed point of a countable family of nonexpansive mappings which solves the corresponding variational inequality. Our results improve and extend the corresponding ones announced by many others.