Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 284613, 8 pages
Research Article

Strong Convergence of Monotone Hybrid Algorithm for Hemi-Relatively Nonexpansive Mappings

Yongfu Su,1 Dongxing Wang,1 and Meijuan Shang1,2

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China

Received 1 June 2007; Revised 5 September 2007; Accepted 16 October 2007

Academic Editor: Simeon Reich

Copyright © 2008 Yongfu Su 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.


The purpose of this article is to prove strong convergence theorems for fixed points of closed hemi-relatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive mapping, but it cannot be used for hemi-relatively nonexpansive mapping. The results of this paper modify and improve the results of S. Matsushita and W. Takahashi (2005), and some others.