An abstract fixed point theorem for nonexpansive mappings
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- by W. A. Kirk PDF
- Proc. Amer. Math. Soc. 82 (1981), 640-642 Request permission
Abstract:
A class $\mathcal {S}$ of subsets of a bounded metric space is said to be normal if each member of $\mathcal {S}$ contains a nondiametral point. An induction proof is given for the following. Suppose $M$ is a nonempty bounded metric space which contains a class $\mathcal {S}$ of subsets which is countably compact, normal, stable under arbitrary intersections, and which contains the closed balls in $M$. Then every nonexpansive self-mapping of $M$ has a fixed point.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 640-642
- MSC: Primary 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1981-0614894-6
- MathSciNet review: 614894