Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 284613, 8 pages
doi:10.1155/2008/284613

Strong convergence of monotone hybrid algorithm for hemi-relatively nonexpansive mappings

Abstract

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.