Let f S ∈ C[-1,1] change its convexity finitely many times in the interval, say s times, at Ys : -1 < y1 < ⋯ < ys < 1. We estimate the degree of approximation of f by polynomials of degree n, which change convexity exactly at the points Ys. We show that provided n is sufficiently large, depending on the location of the points Ys, the rate of approximation is estimated by the third Ditzian-Totik modulus of smoothness of f multiplied by a constant C(s), which depends only on s.
- Coconvex polynomial approximation
- Jackson estimates