NONEXPANSIVE MAPPINGS ON HILBERT'S METRIC SPACES

作者：Lemmens Bas^*

来源：Topological Methods in Nonlinear Analysis, 2011, 38(1): 45-58.

• Nonexpansive mappings
• Hilbert's metric
• periodic orbits
• hyperbolic plane
• simplices
• nonlinear mappings on cones

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.

• 出版日期2011-9