More on comonotone polynomial approximation

D. Leviatan, I. A. Shevchuk

Research output: Contribution to journalArticlepeer-review

Abstract

The main achievement of this paper is that we show, what was to us, a surprising conclusion, namely, twice continuously differentiable functions in (0, 1) (with some regular behavior at the endpoints) which change monotonicity at least once in the interval, are approximable better by comonotone polynomials, than are such functions that are merely monotone. We obtain Jackson-type estimates for the comonotone polynomial approximation of such functions that are impossible to achieve for monotone approximation.

Original languageEnglish
Pages (from-to)475-486
Number of pages12
JournalConstructive Approximation
Volume16
Issue number4
DOIs
StatePublished - 2000

Keywords

  • Comonotone approximation by polynomials
  • Degree of approximation

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