Weak convergence of a primal-dual algorithm for split common fixed-point problems in Hilbert spaces

In this paper, we use the dual variable to propose a new iterative algorithm for solving the split common fixed-point problem of quasi-nonexpansive mappings in real Hilbert spaces. Under suitable conditions, we establish a weak convergence theorem of the proposed algorithm and obtain a related result for the split common fixed-point problem of firmly quasi-nonexpansive mappings. Some numerical experiments are given to illustrate the efficiency of the proposed iterative algorithm.