Copyright © 2009 Yonghong Yao 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.
Let be a real Hilbert space, let , be two nonexpansive mappings such that , let be a contractive mapping, and let be a strongly positive linear bounded operator on . In this paper, we suggest and consider the strong converegence analysis of a new two-step iterative algorithms for finding the approximate solution of two nonexpansive mappings as , , is a real number and , are two sequences in satisfying the following control conditions: (C1) , (C3) , then . We also discuss several special cases of this iterative algorithm.