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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.

Information

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
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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