Abstract
We prove that the iterates of certain periodic nonexpansive operators in l1 uniformly converge to zero in l∞ norm. As a by-product we show that, for any solution x(t) of the equation x(t)= −sign(x(t-1))f(x()), t≥0, x|[−1,0]∈C[−1,0] where f:ℝ→(−1, 1) is locally Lipschitz, the number of zeros of x(t) on any unit interval becomes finite after a period of time, with the single exception of the case f(0)=0 and x(t)≡0.
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