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A Note on a Sequence of Contraction Mappings

Published online by Cambridge University Press:  20 November 2018

S.P. Singh  and
W. Russell
S.P. Singh
Affiliation:
Memorial University of Newfoundland, St. John'sNewfoundland
W. Russell
Affiliation:
Memorial University of Newfoundland, St. John'sNewfoundland
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Extract

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Let E be a metric space. A mapping T of the space E into itself is said to be a contraction if there exist s a number k, with 0 ≤ k < 1 such that

for any two points x, y ∈ E. Every contraction mapping is continuous.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 513 - 516
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Bonsall, F. F., Lectures on some fixed point theorems of cunctional analysis. (Tata Institute of Fundamental Research, Bombay, 1962.)Google Scholar
2. Edelstein, M., On fixed and periodic points under contractive mappings. Jour. Lond. Math. Soc. 37 (1962) 74–79.Google Scholar