Functiones et Approximatio Commentarii Mathematici

Some properties of the generalized Favard-Durrmeyer operators

Grzegorz Nowak and Paulina Pych-Taberska

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Abstract

The Durrmeyer modification $\tilde{F}_{n}f$ of the generalized Favard operators in some weighted function spaces are considered. The rate of convergence of $\tilde{F}_{n}f(x)$ at the Lebesgue points $x$ of $f$ is estimated. In particular, a corresponding estimate in the class of functions $f$ of bounded $p$-th power variation is deduced.

Article information

Source
Funct. Approx. Comment. Math., Volume 29 (2001), 103-112.

Dates
First available in Project Euclid: 29 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.facm/1538186721

Digital Object Identifier
doi:10.7169/facm/1538186721

Mathematical Reviews number (MathSciNet)
MR2135601

Subjects
Primary: 41A35: Approximation by operators (in particular, by integral operators)
Secondary: 41A25: Rate of convergence, degree of approximation

Keywords
Favard-Durrmeyer operator rate of convergence Lebesgue point $p$-th power variation

Citation

Nowak, Grzegorz; Pych-Taberska, Paulina. Some properties of the generalized Favard-Durrmeyer operators. Funct. Approx. Comment. Math. 29 (2001), 103--112. doi:10.7169/facm/1538186721. https://projecteuclid.org/euclid.facm/1538186721


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