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On Fixed and Periodic Points Under Certain Sets of Mappings

Published online by Cambridge University Press:  20 November 2018

R.D. Holmes
R.D. Holmes*
Affiliation:
University of Alberta Edmonton, Alberta
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Let (X, d) be a metric space and f a mapping of X into itself. D.F. Bailey [l] considered a class of mappings f satisfying the condition: ∀x, y ∈ X, x ≠ y,

(1.1)

where I+ denotes the set of positive integers.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 813 - 822
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Bailey, D. F., Some theorems on contractive mappings. J. Lond. Math. Soc. 41 (1966) 101–106.Google Scholar
2. Meyers, P. R., On the converse to the contraction mapping principle. (Ph.D. Thesis, U. of Maryland, 1966).Google Scholar
3. Sehgal, V. M., A fixed point theorem for local contraction mappings. Amer. Math. Soc. Notices 12 (1965) 461.Google Scholar