TY - JOUR
T1 - Uniform convexity, normal structure and the fixed point property of metric spaces
AU - Matsuzaki, Katsuhiko
N1 - Funding Information:
This work was supported by JSPS KAKENHI 24654035 .
Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2015/12
Y1 - 2015/12
N2 - 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.
AB - 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.
KW - Bounded orbit
KW - Circumcenter
KW - Fixed point property
KW - Isometric action
KW - Normal structure
KW - Uniform convexity
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U2 - 10.1016/j.topol.2015.05.039
DO - 10.1016/j.topol.2015.05.039
M3 - Article
AN - SCOPUS:84930038586
SN - 0166-8641
VL - 196
SP - 684
EP - 695
JO - Topology and its Applications
JF - Topology and its Applications
ER -