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Topological Homotheties on Compact Metrizable Spaces
Published online by Cambridge University Press: 20 November 2018
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Notation and definitions.
Definition 1. Let (X, ρ) be a metric space and ϕ: X → X a continuous self-mapping of X. We shall call ϕ and α-contraction on (X, ρ) if and only if α ϵ [0,1) and 
. We shall call ϕ an α-homothety on (X, ρ) if and only if α > 0 and 
.
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- Research Article
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- Copyright © Canadian Mathematical Society 1968
References
2.
Janos, L., Converse of the theorem on contracting mapping, Notices Amer. Math. Soc. 11 1964), 224.Google Scholar
3.
Janos, L., A converse of Banach's contraction theorem, Proc. Amer. Math. Soc. 18 (1967), 287–289.Google Scholar
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