Convergence comparison of several iteration algorithms for the common fixed point problems

Abstract

We discuss the following viscosity approximations with the weak contraction A for a nonexpansive mapping sequence {Tn}, yn = anAyn + (1 - an) Tnyn, xn+1 = anAxn + (1 - an) 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.