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Another Proof of the Contraction Mapping Principle

Published online by Cambridge University Press:  20 November 2018

D.W. Boyd  and
J. S. W. Wong
D.W. Boyd
Affiliation:
University of Wisconsin
J. S. W. Wong
Affiliation:
University of Wisconsin
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In a recent note of Kolodner [2], the Cantor Intersection Theorem is used to give an alternative proof of the well known Contraction Mapping Principle. Kolodner applied Cantor's theorem first to a bounded metric space and then reduced the general case to this special case. Sometime ago, we found a somewhat different proof of the Contraction Mapping Principle using Cantor's theorem. Since our proof seems somewhat more direct we propose to present it here.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 4 , October 1968 , pp. 605 - 606
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Edelstein, M., An extension of Banach's Contraction Principle. Proc. Amer. Math. Soc, 12 (1961) 7-10.Google Scholar
2. Kolodner, I.I., On the proof of the Contraction Mapping Theorem. Amer. Math. Monthly, 74 (1967) 1212-1213.Google Scholar