Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 351265, 12 pages
Research Article

A Strong Convergence Theorem for a Family of Quasi-ϕ-Nonexpansive Mappings in a Banach Space

1Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
2College of Mathematics and Computer Science, Yanan University, Yanan 716000, China

Received 26 May 2009; Revised 29 August 2009; Accepted 14 September 2009

Academic Editor: Nan-jing Huang

Copyright © 2009 Haiyun Zhou and Xinghui Gao. 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 paper is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-ϕ-nonexpansive mappings. The strong convergence theorem is proven in the more general reflexive, strictly convex, and smooth Banach spaces with the property (K). The results of this paper improve and extend the results of S. Matsushita and W. Takahashi (2005), X. L. Qin and Y. F. Su (2007), and others.