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The Fixed Point Set of Real Multi-Valued Contraction Mappings

Published online by Cambridge University Press:  20 November 2018

Arthur S. Finbow
Arthur S. Finbow*
Affiliation:
Dalhousie University, Halifax, Nova Scotia
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Let (X, d1) and (Y, d2) be metric spaces. A mapping f:X→Y is said to be a Lipschitz mapping if there exists a real number λ such that

for each x,y∊X. We call λ a Lipschitz constant for f. If λ∊[0, 1), f is called a contraction mapping. Throughout this note CB(Y) denotes the set of closed and bounded subsets of Y equipped with the Hausdorff metric induced by d2.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 507 - 511
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Nadler, S. B. Jr, Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488.Google Scholar
2. Helga, Schirmer, Properties of the fixed point set of contractive multi-functions, Canad. Math. Bull. 13 (1970), 169-173.Google Scholar