A nonlinear Perron-Frobenius theorem
Robert Sine · Proceedings of the American Mathematical Society · 1990
If T 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 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 {L_p} space with 1 > p > ∞ 1 > p > \infty .