Uniform convexity, normal structure and the fixed point property of metric spaces

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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.

Original languageEnglish
Pages (from-to)684-695
Number of pages12
JournalTopology and its Applications
Volume196
DOIs
Publication statusPublished - 2015 Dec

Keywords

  • Bounded orbit
  • Circumcenter
  • Fixed point property
  • Isometric action
  • Normal structure
  • Uniform convexity

ASJC Scopus subject areas

  • Geometry and Topology

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