Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions - Pleshakov, M. G.; Popov, P. A. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We consider a 2π-periodic function f continuous on \(R\) and changing its sign at 2s points y i ∈ [−π, π). For this function, we prove the existence of a trigonometric polynomial T n of degree ≤n that changes its sign at the same points y i and is such that the deviation | f(x) − T n(x) | satisfies the second Jackson inequality.