Abstract and Applied Analysis
Volume 2012 (2012), Article ID 965751, 11 pages
http://dx.doi.org/10.1155/2012/965751
Research Article

Iterative Algorithm and Δ -Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces

J. F. Tang,1 S. S. Chang,2 H. W. Joseph Lee,3 and C. K. Chan3

1Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China
2College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
3Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong

Received 9 July 2012; Accepted 9 August 2012

Academic Editor: Yongfu Su

Copyright © 2012 J. F. Tang 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

The main purpose of this paper is first to introduce the concept of total asymptotically nonexpansive mappings and to prove a Δ -convergence theorem for finding a common fixed point of the total asymptotically nonexpansive mappings and the asymptotically nonexpansive mappings. The demiclosed principle for this kind of mappings in CAT(0) space is also proved in the paper. Our results extend and improve many results in the literature.