Journal of Applied Mathematics
Volume 2012 (2012), Article ID 474031, 15 pages
Research Article

Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞 -Uniformly Smooth and Strictly Convex Banach Spaces

Department of Mathematics, Hubei Normal University, Hubei, Huangshi 435002, China

Received 24 April 2012; Accepted 23 June 2012

Academic Editor: Hong-Kun Xu

Copyright © 2012 Meng Wen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in 𝑞 -uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.