Open Access

Fixed point theorems in spaces and -trees

Fixed Point Theory and Applications20042004:738084

https://doi.org/10.1155/S1687182004406081

Received: 10 June 2004

Published: 26 December 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.

Authors’ Affiliations

(1)
Department of Mathematics, The University of Iowa

Copyright

© Kirk 2004