Copyright © 2012 Yanrong Yu and Delei Sheng. 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

Based on the recent work by Censor and Segal (2009 J. Convex Anal.16), and inspired by Moudafi (2010 Inverse Problems 26), we modify the algorithm of demicontractive operators proposed by Moudafi and study the modified algorithm for the class of firmly pseudodemicontractive operators to solve the split common fixed-point problem in a Hilbert space. We also give the strong convergence theorem under some appropriate conditions. Our work improves and/or develops the work of Moudafi, Censor and Segal, and other results.