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

研究成果査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)684-695
ページ数12
ジャーナルTopology and its Applications
196
DOI
出版ステータスPublished - 2015 12

ASJC Scopus subject areas

  • 幾何学とトポロジー

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