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Asymptotic behavior of nonexpansive mappings in finite dimensional normed spaces

Author(s): Brian Lins
Journal: Proc. Amer. Math. Soc. 137 (2009), 2387-2392.
MSC (2000): Primary 47H09
Posted: December 23, 2008
MathSciNet review: 2495273
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Abstract: If is a finite dimensional real normed space, is a closed convex subset of and $f:C \rightarrow C$ is nonexpansive with respect to the norm on , then we show that either has a fixed point in 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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