College of Mathematics and Information Science, Henan Normal University, 453007, China
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.
We discuss the following viscosity approximations
with the weak contraction for a non-expansive mapping sequence , , . 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.