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On representations of selfmappings by contractions

Published online by Cambridge University Press:  17 April 2009

Ludvik Janos
Ludvik Janos
Affiliation:
Department of Mathematics, University of Montana, Missoula, Montana, USA.
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Abstract

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It is shown that any selfmapping (X, f) can be equivariantly and naturally embedded in the selfmapping of the form (X1, f1) ∪ (x2, f2) × (Y, g) where f1 and f2 are contractive relative to suitably chosen metrics and g is a bijection with all points periodic.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 1 , August 1974 , pp. 37 - 41
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Bessaga, C., “On the converse of the Banach ‘fixed-point principle’”, Colloq. Math. 7 (1959), 41–43.Google Scholar
[2]de Groot, J. and de Vries, H., “Metrization of a set which is mapped into itself”, Quart. J. Math. Oxford (2) 9 (1958), 144–148.Google Scholar
[3]Janos, Ludvik, “An application of combinatorial techniques to a topological problem”, Bull. Austral. Math. Soc. 9 (1973), 439–443.Google Scholar