On uniformly Lipschitzian multivalued mappings in Banach and metric spaces

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 ( T n ( x ) , T n ( 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 , p...

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Bibliographic Details
Published in:Nonlinear analysis 2010-02, Vol.72 (3), p.2080-2085
Main Authors: Khamsi, M.A., Kirk, W.A.
Format: Article
Language:English
Subjects:
CAT spaces
Exact sciences and technology
Fixed point
Functional analysis
General topology
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Multivalued mappings
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Uniformly convex Banach spaces
Uniformly convex metric spaces
Uniformly Lipschitzian mapping
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Summary: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 ( T n ( x ) , T n ( 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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.10.008