Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 307245, 19 pages
doi:10.1155/2010/307245
Research Article

Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces

Murat Ozdemir, Sezgin Akbulut, and Hukmi Kiziltunc

Department of Mathematics, Faculty of Science, Ataturk University, Erzurum 25240, Turkey

Received 21 October 2009; Accepted 20 January 2010

Academic Editor: Guang Zhang

Copyright © 2010 Murat Ozdemir 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.

Abstract

We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al. (2003), Wang (2006), Shahzad (2005), and Thianwan (2008).