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Periodic Points and Contractive Mappings

Published online by Cambridge University Press:  20 November 2018

Tsu-Teh Hsieh  and
Kok-Keong Tan
Tsu-Teh Hsieh
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan, Canada
Kok-Keong Tan
Affiliation:
Dalhousie University, Halifax, Nova Scotia, Canada
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Let X be a non-empty set and f:X→X. A point x ∈ X is (i) a fixed point off f(x)=x, and (ii) a periodic point of f iff there is a positive integer N such that fN(x)=x. Also a periodic orbit of f is the (finite) set {x, f(x), f2(x),…} where x is a periodic point of f.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 209 - 211
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bryant, J. and Guseman, L. F. Jr, Fixed points of subcontractive mappings. To appear.Google Scholar
2. Edelstein, M., On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), pp. 74-79.Google Scholar
3. Ng, K. W., A remark on contractive mappings, Canadian Math. Bull. 13 (1970), pp. 111-113.Google Scholar
4. Tan, K. K., Fixed point theorems for nonexpansive mappings, Pacific J. Math. 14 (1972), pp. 829-842.Google Scholar