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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A nonlinear Perron-Frobenius theorem


Author: Robert Sine
Journal: Proc. Amer. Math. Soc. 109 (1990), 331-336
MSC: Primary 47H09; Secondary 47H10, 58F11
MathSciNet review: 948156
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Abstract: If $ T$ is a nonexpansive map on a domain in a finite-dimensional sup norm space then there is a universal bound on the periods of periodic points. This yields the same result for $ T$ nonexpansive on a domain in a finite-dimensional Banach space which has a polyhedral unit ball. Similar results are obtained for certain nonexpansive maps defined on all of an infinite-dimensional $ {L_p}$ space with $ 1 < p < \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1990-0948156-X
Keywords: Recurrence, periodic point, nonexpansive map, sup norm space
Article copyright: © Copyright 1990 American Mathematical Society