- Research Article
- Open access
- Published:
Fixed point theorems in
spaces and
-trees
Fixed Point Theory and Applications volume 2004, Article number: 738084 (2004)
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kirk, W. Fixed point theorems in spaces and
-trees.
Fixed Point Theory Appl 2004, 738084 (2004). https://doi.org/10.1155/S1687182004406081
Received:
Published:
DOI: https://doi.org/10.1155/S1687182004406081