Asymptotic behavior of nonexpansive mappings in finite dimensional normed spaces
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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 $x \in C$.References
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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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2387-2392
- MSC (2000): Primary 47H09
- DOI: https://doi.org/10.1090/S0002-9939-08-09779-7
- MathSciNet review: 2495273