Lemmens, Bas (2011) Non-expansive mappings on Hilbert’s metric spaces. Topological Methods in Nonlinear Analysis, 38 (1). pp. 45-58. ISSN 1230-3429.
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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.
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus|
|Depositing User:||Bas Lemmens|
|Date Deposited:||18 Nov 2011 14:43|
|Last Modified:||10 Jan 2012 11:50|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/28447 (The current URI for this page, for reference purposes)|
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