2016-11-142016-11-142013-12-15Espínola García, R. y Pia̧tek, B. (2013). The fixed point property and unbounded sets in CAT(0) spaces. Journal of Mathematical Analysis and Applications, 408 (2), 638-654.0022-247Xhttp://hdl.handle.net/11441/48490In this work we study the fixed point property for nonexpansive self-mappings defined on convex and closed subsets of a CAT(0) space. We will show that a positive answer to this problem is very much linked with the Euclidean geometry of the space while the answer is more likely to be negative if the space is more hyperbolic. As a consequence we extend a very well known result of W.O. Ray on Hilbert spaces.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Nonexpansive mappingsFixed pointsUnbounded convex setsCAT(0) spacesBanach-Steinhaus theoreminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/j.jmaa.2013.06.038https://idus.us.es/xmlui/handle/11441/48490