Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 367274, 11 pages
Research Article

Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces

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

Received 23 July 2009; Accepted 30 November 2009

Academic Editor: Tomonari Suzuki

Copyright © 2010 W. Laowang 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.


Suppose that K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T:KX be a nonexpansive nonself mapping with F(T):={xK:Tx=x}. Suppose that {xn} is generated iteratively by x1K, xn+1=P((1αn)xnαnTP[(1βn)xnβnTxn]), n1, where {αn} and {βn} are real sequences in [ε,1ε] for some ε(0,1). Then {xn}Δ-converges to some point x in F(T). This is an analog of a result in Banach spaces of Shahzad (2005) and extends a result of Dhompongsa and Panyanak (2008) to the case of nonself mappings.