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 -