A nonlinear Perron-Frobenius theorem

Sine, Robert

doi:10.1090/S0002-9939-1990-0948156-X

A nonlinear Perron-Frobenius theorem
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Proc. Amer. Math. Soc. 109 (1990), 331-336 Request permission

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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