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Proceedings of the American Mathematical Society

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On firmly nonexpansive mappings


Author: Ryszard Smarzewski
Journal: Proc. Amer. Math. Soc. 113 (1991), 723-725
MSC: Primary 47H09; Secondary 47H10
MathSciNet review: 1050023
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Abstract: It is shown that any $ \lambda $-firmly, $ 0 < \lambda < 1$ , nonexpansive mapping $ T:C \to C$ has a fixed point in $ C$ whenever $ C$ is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1050023-1
Keywords: Firmly nonexpansive mappings, fixed-point theorems, nonconnected domains
Article copyright: © Copyright 1991 American Mathematical Society