On the Edelstein Contractive Mapping Theorem
Keyword(s):
AbstractLet X be a metrizable topological space and f:X→X a continuous selfmapping such that for every x ∈ X the sequence of iterates {fn(x)} converges. It is proved that under these conditions the following two statements are equivalent:1. There is a metrization of X relative to which f is contractive in the sense of Edelstein.2. For any nonempty f-invariant compact subset Y of X the intersection of all iterates fn(Y) is a one-point set. The relation between this type of contractivity and the Banach contraction principle is also discussed.
2001 ◽
Vol 130
(4)
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pp. 927-933
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2001 ◽
pp. 1-23
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2002 ◽
Vol 273
(1)
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pp. 112-120
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2016 ◽
Vol 09
(03)
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pp. 873-875
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2020 ◽
Vol 2020
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pp. 1-19
1978 ◽
Vol 69
(1)
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pp. 166-166
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