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

    Research output: Contribution to journalArticle

    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
    JournalTopology and its Applications
    DOIs
    Publication statusAccepted/In press - 2014 Jan 31

    Fingerprint

    Uniform Convexity
    Normal Structure
    Fixed Point Property
    Metric space
    Uniformly Convex
    Complete Metric Space
    Isometric
    Geodesic
    Automorphisms
    Orbit
    Fixed point
    Subset
    Formulation

    Keywords

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

    ASJC Scopus subject areas

    • Geometry and Topology

    Cite this

    @article{0b9ddb4e4fda48899b768c8a1ef34e0f,
    title = "Uniform convexity, normal structure and the fixed point property of metric spaces",
    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 = "Bounded orbit, Circumcenter, Fixed point property, Isometric action, Normal structure, Primary, Secondary, Uniform convexity",
    author = "Katsuhiko Matsuzaki",
    year = "2014",
    month = "1",
    day = "31",
    doi = "10.1016/j.topol.2015.05.039",
    language = "English",
    journal = "Topology and its Applications",
    issn = "0166-8641",
    publisher = "Elsevier",

    }

    TY - JOUR

    T1 - Uniform convexity, normal structure and the fixed point property of metric spaces

    AU - Matsuzaki, Katsuhiko

    PY - 2014/1/31

    Y1 - 2014/1/31

    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 - Primary

    KW - Secondary

    KW - Uniform convexity

    UR - http://www.scopus.com/inward/record.url?scp=84930038586&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84930038586&partnerID=8YFLogxK

    U2 - 10.1016/j.topol.2015.05.039

    DO - 10.1016/j.topol.2015.05.039

    M3 - Article

    AN - SCOPUS:84930038586

    JO - Topology and its Applications

    JF - Topology and its Applications

    SN - 0166-8641

    ER -