%0 Journal Article %T A Note on Geodesically Bounded -Trees %A W. A. Kirk %J Fixed Point Theory and Applications %D 2010 %I Springer %R 10.1155/2010/393470 %X It is proved that a complete geodesically bounded R-tree is the closed convex hull of the set of its extreme points. It is also noted that if X is a closed convex geodesically bounded subset of a complete R-tree Y, and if a nonexpansive mapping T:X¡úY satisfies inf {d(x,T(x)):x¡ÊX}=0, then T has a fixed point. The latter result fails if T is only continuous. %U http://dx.doi.org/10.1155/2010/393470