In this paper, we propose and analyze a three-step general iteration method which is special case of an proposed in (S. Thianwan S. Suantai, Convergence criteria new with errors for nonexpansive nonself-mappings, Comput. Math. Appl. 52 (2006), 1107-1118). Here intend to study directly the accumulation, estimation control random newly method. We give conditions under accumulated-error our bounde...