Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 268780, 14 pages
doi:10.1155/2010/268780
Research Article

Demiclosed Principle for Asymptotically Nonexpansive Mappings in CAT(0) Spaces

B. Nanjaras and B. Panyanak

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 21 August 2009; Accepted 18 January 2010

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 B. Nanjaras and B. Panyanak. 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 prove the demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces. As a consequence, we obtain a Δ-convergence theorem of the Krasnosel'skii-Mann iteration for asymptotically nonexpansive mappings in this setting. Our results extend and improve many results in the literature.