On uniformly Lipschitzian multivalued mappings in Banach and metric spaces

M. A. Khamsi, W. A. Kirk

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Abstract

Let (X, d) be a metric space. A mapping T : X → X is said to be uniformly Lipschitzian if there exists a constant k such that d (Tn (x), Tn (y)) ≤ k d (x, y) for all x, y ∈ X and n ≥ 1. It is known that such mappings always have fixed points in certain metric spaces for k > 1, provided k is sufficiently near 1. These spaces include uniformly convex metric and Banach spaces, as well as metric spaces having 'Lifšic characteristic' greater than 1. A uniformly Lipschitzian concept for multivalued mappings is introduced in this paper, and multivalued analogues of these results are obtained.

Original languageBritish English
Pages (from-to)2080-2085
Number of pages6
JournalNonlinear Analysis, Theory, Methods and Applications
Volume72
Issue number3-4
DOIs
StatePublished - 1 Feb 2010

Keywords

  • CAT(0) spaces
  • Fixed point
  • Multivalued mappings
  • Uniformly convex Banach spaces
  • Uniformly convex metric spaces
  • Uniformly Lipschitzian mapping

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