The strong convergence theorems for split common fixed point problem ofasymptotically nonexpansive mappings in Hilbert spaces

In this paper, an iterative algorithm is introduced to solve the split common fixedpoint problem for asymptotically nonexpansive mappings in Hilbert spaces. Theiterative algorithm presented in this paper is shown to possess strong convergencefor the split common fixed point problem of asymptotically nonexpansive mappingsalthough the mappings do not have semi-compactness. Our results improve and developprevious methods for solving the split common fixed point problem. MSC: 47H09, 47J25.