Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 170701, 15 pages
doi:10.1155/2010/170701
Research Article

Modified Hybrid Algorithm for a Family of Quasi-ϕ-Asymptotically Nonexpansive Mappings

Yongchun Xu,1 Xin Zhang,2 Jinlong Kang,2 and Yongfu Su2

1Department of Mathematics, Hebei North University, Zhangjiakou 075000, China
2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Received 19 March 2010; Accepted 16 August 2010

Academic Editor: L. Górniewicz

Copyright © 2010 Yongchun Xu 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

The purpose of this paper is to propose a modified hybrid projection algorithm and prove strong convergence theorems for a family of quasi-ϕ-asymptotically nonexpansive mappings. The method of the proof is different from the original one. Our results improve and extend the corresponding results announced by Zhou et al. (2010), Kimura and Takahashi (2009), and some others.