Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 681214, 7 pages
doi:10.1155/2011/681214
Research Article

Strong Convergence Theorems by Shrinking Projection Methods for Class 𝔗 Mappings

Qiao-Li Dong,1,2 Songnian He,1,2 and Fang Su3

1College of Science, Civil Aviation University of China, Tianjin 300300, China
2Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China
3Department of Mathematics and Systems Science, National University of Defense Technology, Changsha 410073, China

Received 9 December 2010; Accepted 2 February 2011

Academic Editor: S. Al-Homidan

Copyright © 2011 Qiao-Li Dong 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 prove a strong convergence theorem by a shrinking projection method for the class of 𝔗 mappings. Using this theorem, we get a new result. We also describe a shrinking projection method for a nonexpansive mapping on Hilbert spaces, which is the same as that of Takahashi et al. (2008).