The degree of coconvex polynomial approximation

K. Kopotun, D. Leviatan, I. A. Shevchuk

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)409-415
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - 1999
Externally publishedYes


  • Coconvex polynomial approximation
  • Jackson estimates


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