Copyright © 2012 Juguo Su et al. 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

The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.