Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 783178, 15 pages
doi:10.1155/2010/783178
Research Article

Convergence of Three-Step Iterations Scheme for Nonself Asymptotically Nonexpansive Mappings

Seyit Temir

Department of Mathematics, Art, and Science Faculty, Harran University, 63200 Sanliurfa, Turkey

Received 15 February 2010; Revised 2 May 2010; Accepted 30 June 2010

Academic Editor: Jerzy Jezierski

Copyright © 2010 Seyit Temir. 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

Weak and strong convergence theorems of three-step iterations are established for nonself asymptotically nonexpansive mappings in uniformly convex Banach space. The results obtained in this paper extend and improve the recent ones announced by Suantai (2005), Khan and Hussain (2008), Nilsrakoo and Saejung (2006), and many others.