Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions

  • M. G. Pleshakov
  • P. A. Popov

Abstract

We consider a 2π-periodic function f continuous on \(\mathbb{R}\) 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.
Published
25.01.2004
How to Cite
PleshakovM. G., and PopovP. A. “Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 1, Jan. 2004, pp. 123-8, https://umj.imath.kiev.ua/index.php/umj/article/view/3734.
Section
Short communications