In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm forapproximating common fixed points for asymptotically nonexpansive mappings, published to Fixed Point Theory and Applications 2007 :1-9], and many others.

Keywords: asymptotically quasi-nonexpansive type nonself-mapping, completely continuous, uniformly convex Banach space, smooth Banach space, uniformly L-Lipschitzian nonself-mapping, weakly inward, one-step iterative scheme