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Let C be a bounded convex subset in a uniformly convex Banach space X, x0, un∈C, then xn+1=Snxn, where Sn=αn0I+αn1T+αn2T2+…+αnkTk+γnun, αni≥0, 0<α≤αn0≤b<1, ∑ki=0αni+γn=1, and n≥1. It is proved that xn converges to a fixed point on T if T is a nonexpansive