Closed mappings on complete metric spaces
R. Engelking (1971)
Fundamenta Mathematicae
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Displaying similar documents to “On the converse of Banach 'fixed-point principle'”
Closed mappings on complete metric spaces
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On the Lifshits Constant for Hyperspaces
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The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.