Lp approximation with rates by multivariate generalized discrete singular operators

George A. Anastassiou and Merve Kester

Applied Mathematics and Computation, 2015, vol. 265, issue C, 652-666

Abstract: Here we give the approximation properties with rates of multivariate generalized discrete versions of Picard, Gauss–Weierstrass, and Poisson–Cauchy singular operators over RN,N ≥ 1. We treat both the unitary and non-unitary cases of the operators above. We derive quantitatively Lp convergence of these operators to the unit operator by involving the Lp higher modulus of smoothness of an Lp function.

Keywords: Multivariate discrete singular operator; Lp modulus of smoothness; Lp convergence (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:652-666

DOI: 10.1016/j.amc.2015.05.073

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