Abstract. 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 for approximating common fixed points for asymptotically nonexpansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.
The purpose of this article is to prove strong convergence theorems for mapping of asymptotically quasi-nonexpansive types in a Hilbert space according to hybrid methods. The results obtained in this paper extend and improve upon those recently announced by Qin, X., Su, Y. and Shang, M. (Qin, X. et al., 2008), and many others.
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