Fixed Point Theory and Applications (Jan 2009)

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

  • Yisheng Song,
  • Xiao Liu

DOI
https://doi.org/10.1155/2009/824374
Journal volume & issue
Vol. 2009

Abstract

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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.