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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic behavior of nonexpansive mappings in finite dimensional normed spaces


Author: Brian Lins
Journal: Proc. Amer. Math. Soc. 137 (2009), 2387-2392
MSC (2000): Primary 47H09
Published electronically: December 23, 2008
MathSciNet review: 2495273
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Abstract: If $ X$ is a finite dimensional real normed space, $ C$ is a closed convex subset of $ X$ and $ f:C \rightarrow C$ is nonexpansive with respect to the norm on $ X$, then we show that either $ f$ has a fixed point in $ C$ or there is a linear functional $ \varphi \in X^*$ such that $ \lim_{k \rightarrow \infty} \varphi(f^k(x)) = \infty$ for all $ x \in C$.


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Additional Information

Brian Lins
Affiliation: Department of Mathematics and Computer Science, Hampden-Sydney College, Hampden-Sydney, Virginia 23943
Email: blins@hsc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09779-7
PII: S 0002-9939(08)09779-7
Received by editor(s): July 23, 2007
Received by editor(s) in revised form: September 28, 2008
Published electronically: December 23, 2008
Communicated by: Marius Junge
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.