Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 351265, 12 pages
doi:10.1155/2009/351265
A Strong Convergence Theorem for a Family of Quasi-ϕ-Nonexpansive Mappings in a Banach Space
Haiyun Zhou1
and Xinghui Gao2
1Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
2College of Mathematics and Computer Science, Yanan University, Yanan 716000, China
Abstract
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.