Nonexpansive Periodic Operators in l1 with Application to Superhigh-Frequency Oscillations in a Discontinuous Dynamical System with Time Delay

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()), t0, x|_[–1,0]C[–1,0] where f:(–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.