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Fixed Points of Uniformly Lipschitzian Mappings in Metric spaces

Dhompongsa, Sompong and Kirk, William A. and Sims, Brailey (2006) Fixed Points of Uniformly Lipschitzian Mappings in Metric spaces. Nonlinear Analysis, 65 (4). pp. 762-772. ISSN 0362-546X

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    Abstract

    Two fixed point theorems for uniformly lipschitzian mappings in metric spaces, due respectively to E. Lifsic and to T.-C. Lim and H.-K. Xu, are compared within the framework of the so-called CAT(0) spaces. It is shown that both results apply in this setting, and that Lifsic's theorem gives a sharper result. Also, a new property is introduced that yields a fixed point theorem for uniformly lipschitzian mappings in a class of hyperconvex spaces, a class which includes those possessing property (P) of Lim and Xu.

    Item Type: Article
    Uncontrolled Keywords: Uniformly lipschitzian mappings; Fixed points; CAT(0) spaces; Hyperconvex spaces
    Subjects: 47-xx Operator theory > 47Hxx Nonlinear operators and their properties
    54-xx General topology > 54Exx Spaces with richer structures
    Faculty: UNSPECIFIED
    Depositing User: Associate Professor Brailey Sims
    Date Deposited: 06 Apr 2011 16:58
    Last Modified: 06 Apr 2011 16:58
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/852

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