Pointwise estimates for convex polynomial approximation

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For a convex function f ϵ C[—l, 1] we construct a sequence of convex polynomials pn of degree not exceeding n such that |f(x) — pn(x)| ≤ Cw2(f, √l —x2n), —1 ≤ x ≤ 1. If in addition f is monotone it follows that the polynomials are also monotone thus providing simultaneous monotone and convex approximation.

Original languageEnglish
Pages (from-to)471-474
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - Nov 1986


  • Degree of convex polynomial approximation
  • Jackson-Timan-TeljakowskiĬ type estimates
  • Moduli of smoothness
  • The Peetre kernel


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