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

We discuss the following viscosity approximations with the weak contraction A for a non-expansive mapping sequence {Tn}, yn αnAyn 1 − αnTnyn, xn1 αnAxn 1 − αnTnxn. 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. Copyright q 2009 Y. Song and X. 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. 1