Coconvex approximation of periodic functions
AbstractThe Jackson inequality E n (f ) ≤ c ω 3 (f , π / n ) connects the value of the best uniform approximation E n (f ) of a 2π-periodic function f : R → R by trigonometric polynomials of order ≤ n — 1 with its third modulus of continuity ω 3 (f, t ).
In the present paper, we show that this inequality is true if continuous 2π-periodic functions that change their convexity on [—π, π) only at every point of a fixed finite set consisting of the even number of points are approximated by polynomials coconvex to them.
How to Cite
Zalizko, V. D. “Coconvex Approximation of Periodic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 1, Jan. 2007, pp. 29–43, https://umj.imath.kiev.ua/index.php/umj/article/view/3290.