Nonexpansive mappings on Hilbert's metric spaces
Keywords
Nonexpansive mappings, Hilbert's metric, periodic orbits, hyperbolic plane, simplices, nonlinear mappings on conesAbstract
This paper deals with the iterative behavior of nonexpansive mappings on Hilbert's metric spaces $(X,d_X)$. We show that if $(X,d_X)$ is strictly convex and does not contain a hyperbolic plane, then for each nonexpansive mapping, with a fixed point in $X$, all orbits converge to periodic orbits. In addition, we prove that if $X$ is an open $2$-simplex, then the optimal upper bound for the periods of periodic points of nonexpansive mappings on $(X,d_X)$ is $6$. The results have applications in the analysis of nonlinear mappings on cones, and extend work by Nussbaum and others.Downloads
Published
2011-04-23
How to Cite
1.
LEMMENS, Bas. Nonexpansive mappings on Hilbert’s metric spaces. Topological Methods in Nonlinear Analysis. Online. 23 April 2011. Vol. 38, no. 1, pp. 45 - 58. [Accessed 28 March 2024].
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