The Degree of Coconvex Polynomial Approximation
نویسندگان
چکیده
Let f ∈ 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.
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