## Abstract

For a function f ∈ L_{p}[-1, 1], 0 < p < ∞, with finitely many sign changes, we construct a sequence of polynomials P_{n} ∈ ∏_{n} which are copositive with f and such that ∥f-P_{n}∥_{p} ≤ Cω_{φ}(f, (n + 1)^{1})_{p}, where ω_{φ}(f, t)_{p} denotes the Ditzian-Totik modulus of continuity in L_{p} metric. It was shown by S. P. Zhou that this estimate is exact in the sense that if f has at least one sign change, then ω_{φ} cannot be replaced by ω^{2} if 1 < p < ∞. In fact, we show that even for positive approximation and all 0 < p < ∞ the same conclusion is true. Also, some results for (co)positive spline approximation, exact in the same sense, are obtained.

Original language | English |
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Pages (from-to) | 320-334 |

Number of pages | 15 |

Journal | Journal of Approximation Theory |

Volume | 86 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1996 |

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