## Abstract

The order of positive and copositive spline approximation in the L_{p}-norm, 1 ≤ p < ∞, is studied; the main results are 1. (1) the error of positive approximation by splines is bounded by Cω_{2}(f, 1 n)_{p} if f has a nonnegative extension; 2. (2) the order deteriorates to ω_{1} if f does not have such an extension; 3. (3) the error of copositive spline approximation is bounded by Cω(f, 1 n)_{p}; 4. (4) if f is also continuous, the error in (3) can be estimated in terms of the third τ-modulus τ_{3}(f, 1 n)_{p}. All constants in the error bounds are absolute.

Original language | English |
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Pages (from-to) | 137-146 |

Number of pages | 10 |

Journal | Computers and Mathematics with Applications |

Volume | 30 |

Issue number | 3-6 |

DOIs | |

State | Published - Sep 1995 |

## Keywords

- Constrained approximation in L space
- Degree of copositive approximation
- Polynomial approximation
- Spline approximation

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