Iterative solutions of the split common fixed point problem for strictly pseudo-contractive mappings

In this paper, we study the the split common fixed point problem in Hilbert spaces. We establish a weak convergence theorem for the method recently introduced by Wang, which extends a existing result from firmly nonexpansive mappings to strictly pseudo-contractive mappings. Moreover, our condition that guarantees the weak convergence is much weaker than that of Wang’s. A strong convergence theorem is also obtained under some additional conditions. As an application, we obtain several new methods for solving various split inverse problems and split equality problems. Numerical examples are included to illustrate the applications in signal processing of the proposed algorithm.