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Weighted L1 approximation on [−1,1] via discrete de la Vallée Poussin means

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  • Themistoclakis, Woula

Abstract

We consider some discrete approximation polynomials, namely discrete de la Vallée Poussin means, which have been recently deduced from certain delayed arithmetic means of the Fourier–Jacobi partial sums, in order to get a near–best approximation in suitable spaces of continuous functions equipped with the weighted uniform norm. By the present paper we aim to analyze the behavior of such discrete de la Vallée means in weighted L1 spaces, where we provide error bounds for several classes of functions, included functions of bounded variation. In all the cases, under simple conditions on the involved Jacobi weights, we get the best approximation order. During our investigations, a weighted L1 Marcinkiewicz type inequality has been also stated.

Suggested Citation

  • Themistoclakis, Woula, 2018. "Weighted L1 approximation on [−1,1] via discrete de la Vallée Poussin means," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 279-292.
    • Handle: RePEc:eee:matcom:v:147:y:2018:i:c:p:279-292
    DOI: 10.1016/j.matcom.2017.06.005
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    Keywords

    Discrete de la Vallée Poussin mean; Weighted L1 polynomial approximation; Modulus of smoothness; Bounded variation function;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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