An abstract fixed point theorem for nonexpansive mappings

Author:
W. A. Kirk

Journal:
Proc. Amer. Math. Soc. **82** (1981), 640-642

MSC:
Primary 54H25

MathSciNet review:
614894

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Abstract: A class of subsets of a bounded metric space is said to be normal if each member of contains a nondiametral point. An induction proof is given for the following. Suppose is a nonempty bounded metric space which contains a class of subsets which is countably compact, normal, stable under arbitrary intersections, and which contains the closed balls in . Then every nonexpansive self-mapping of has a fixed point.

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0614894-6

Keywords:
Fixed point theorem,
nonexpansive mappings

Article copyright:
© Copyright 1981
American Mathematical Society