spaces and 
-trees
Abstract
We show that if 
is a bounded open set in a complete 
space 
, and if 
is nonexpansive, then 
always has a fixed point if there exists 
such that 
for all 
. It is also shown that if 
is a geodesically bounded closed convex subset of a complete 
-tree with 
, and if 
is a continuous mapping for which 
for some 
and all 
, then 
has a fixed point. It is also noted that a geodesically bounded complete 
-tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.