Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 824374, 13 pages
doi:10.1155/2009/824374
Research Article

Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems

Yisheng Song and Xiao Liu

College of Mathematics and Information Science, Henan Normal University, 453007, China

Received 20 January 2009; Accepted 2 May 2009

Academic Editor: Naseer Shahzad

Copyright © 2009 Yisheng Song and Xiao Liu. 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

We discuss the following viscosity approximations with the weak contraction A for a non-expansive mapping sequence {Tn}, yn=αnAyn+(1−αn)Tnyn, xn+1=αnAxn+(1−αn)Tnxn. We prove that Browder's and Halpern's type convergence theorems imply Moudafi's viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern's type iteration and Mouda's viscosity approximations with the weak contraction.