Simultaneous Weighted Approximation with Multivariate Baskakov–Schurer Operators

Antonio-Jesús López-Moreno (), Joaquı́n Jódar-Reyes and José-Manuel Latorre-Palacios
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Antonio-Jesús López-Moreno: Universidad de Jaén
Joaquı́n Jódar-Reyes: Universidad de Jaén
José-Manuel Latorre-Palacios: Universidad de Jaén

A chapter in Mathematical Analysis, Approximation Theory and Their Applications, 2016, pp 483-500 from Springer

Abstract: Abstract We study the properties of weighted simultaneous approximation of multivariate Baskakov–Schurer operators. We obtain quantitative estimates with explicit constants of the weighted approximation error for the partial derivatives. Moreover, we analyze the behavior of the operators with respect to weighted Lipschitz functions. For this purpose, we first compute the best constants, M ∈ ℝ $$M \in \mathbb{R}$$ , in the inequalities of the type A n , p ( 1 + t ) r ≤ M ( 1 + t ) r $$A_{n,p}\left ((1 + \left \vert t\right \vert )^{r}\right ) \leq M(1 + \left \vert t\right \vert )^{r}$$ .

Keywords: Weighted simultaneous approximation; Lipschitz functions; Moduli of continuity; Multivariate operators (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-31281-1_21

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DOI: 10.1007/978-3-319-31281-1_21

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