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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 367274 11 pages doi 10.1155 2010 367274 Research Article Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT 0 Spaces W. Laowang and B. Panyanak Department of Mathematics Faculty of Science Chaing Mai University Chiang Mai 50200 Thailand Correspondence should be addressed to B. Panyanak banchap@chiangmai.ac.th 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 K X be a nonexpansive nonself mapping with F T x e K Tx x 0. Suppose that xn is generated iteratively by X1 e K xn 1 P 1 - an xn anTP 1 - pn xn pnTxn n 1 where an and pn are real sequences in e 1 - e for some e e 0 1 . Then xn A-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. 1. Introduction A metric space X is a CAT 0 space if it is geodesically connected and if every geodesic triangle in X is at least as thin as its comparison triangle in the Euclidean plane. It is well known that any complete simply connected Riemannian manifold having nonpositive sectional curvature is a CAT 0 space. Other examples include Pre-Hilbert spaces R-trees see 1 Euclidean buildings see 2 the complex Hilbert ball with a hyperbolic metric see 3 and many others. For a thorough discussion of these spaces and of the fundamental role they play in geometry see Bridson and Haefliger 1 . The work by Burago et al. 4 contains a somewhat more elementary treatment and by Gromov 5 a deeper study.
