... theproof.AcknowledgmentThis research is supported by Tianjin Natural Science Foundation in China Grant no.06YFJMJC12500.2 Fixed Point Theory and Applicationsfor fixed points of nonexpansive mapping T in Banach ... nonexpansive mappings in uniformly con-vex Banach spaces,” Commentationes Mathematicae Universitatis Carolinae, vol. 30, no. 2, pp. 249–252,1989.4 J. Schu, “Weak and strong convergence to fixed points ... asymptotically nonexpansive mappings, ”Bulletin of the Australian Mathematical Society, vol. 43, no. 1, pp. 153–159, 1991.6 Fixed Point Theory and ApplicationsSince, for any i 1, 2, 3, ,N,xn−...