We prove that the iterates of certain periodic nonexpansive operators in t1 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(*(t - 1))+f(x(t)), t≥0, x| [-1,0] ∈ C[-l,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.
All Science Journal Classification (ASJC) codes
- Differential delay equations
- Nonexpansive operators