## Abstract

We prove that for each convex function ƒ ϵ L_{p}, 0 < p ≤ 1, there exists a convex algebraic polynomial P_{n} of degree ≤n such that [Formula presented] where ω^{Ψ}_{2}(ƒ, t)p is the Ditzian-Totik modulus of smoothness of f(hook) in L_{p}, and C depends only on p. Moreover, if ƒ is also nondecreasing, then the polynomial P_{n} can also be taken to be nondecreasing, thus we have simultaneous monotone and convex approximation in this case.

Original language | English |
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Pages (from-to) | 79-84 |

Number of pages | 6 |

Journal | Journal of Approximation Theory |

Volume | 75 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1993 |

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