Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 976192, 9 pages
doi:10.1155/2011/976192
Research Article

Approximating Fixed Points of Non-Lipschitzian Mappings by Metric Projections

Hossein Dehghan,1 Amir Gharajelo,2 and Davood Afkhamitaba3

1Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Gava Zang, Zanjan 45137-66731, Iran
2Department of Mathematics, Roozbeh Institute of Higher Education, Zanjan 45186-74947, Iran
3Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas 79158-93144, Iran

Received 22 November 2010; Revised 5 February 2011; Accepted 8 February 2011

Academic Editor: Naseer Shahzad

Copyright © 2011 Hossein Dehghan 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 define and study a new iterative algorithm inspired by Matsushita and Takahashi (2008). We establish a strong convergence theorem of the proposed algorithm for asymptotically nonexpansive in the intermediate sense mappings in uniformly convex and smooth Banach spaces by using metric projections. This theorem generalizes and refines Matsushita and Takahashi's strong convergence theorem which was established for nonexpansive mappings.