Coconvex approximation of periodic functions

The Jackson inequality En(f) ≤ c\omega3 ({f,π/n) relates the value of the best uniform approximation En (f) of a continuous 2π-periodic function f: ℝ → ℝ by trigonometric polynomials of degree ≥ n-1 to 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 an even number of points are approximated by polynomials coconvex to them. © Springer Science+Business Media, Inc. 2007.