Abstract and Applied Analysis
Volume 2013 (2013), Article ID 251705, 6 pages
http://dx.doi.org/10.1155/2013/251705
Research Article

-Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Luo Yi Shi,1 Ru Dong Chen,1 and Yu Jing Wu2

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2Tianjin Vocational Institute, Tianjin 300410, China

Received 23 January 2013; Accepted 17 February 2013

Academic Editor: Yisheng Song

Copyright © 2013 Luo Yi Shi 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

New △-convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained. Consider an asymptotically nonexpansive self-mapping of a closed convex subset of a CAT(0) space . Consider the iteration process , where is arbitrary and or for , where . It is shown that under certain appropriate conditions on   △-converges to a fixed point of .