Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424609 | Topology and its Applications | 2015 | 12 Pages |
Abstract
We say that a complete metric space X has the fixed point property if every group of isometric automorphisms of X with a bounded orbit has a fixed point in X. We prove that if X is uniformly convex then the family of admissible subsets of X possesses uniformly normal structure and if so then it has the fixed point property. We also show that from other weaker assumptions than uniform convexity, the fixed point property follows. Our formulation of uniform convexity and its generalization can be applied not only to geodesic metric spaces.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Katsuhiko Matsuzaki,