Another look at the split common fixed point problem for demicontractive operators

In this article, we take a look at the recent results of Moudafi (Inverse Probl 26:587-600, 2010), Tang et al. (Math Model Anal 17:457-466, 2012) and Wang and Cui (Math Model Anal 18:537-542, 2013), which weak convergence results were obtained for the split common fixed point problem for demicontractive mappings. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings and then prove strong convergence of the sequence in real Hilbert spaces. We also apply our results to the split common null point problem in real Hilbert spaces. Finally, we give numerical results to demonstrate its convergence.