Simultaneous approximation by Bernstein polynomials with integer coefficients

We prove that several forms of the Bernstein polynomials with integer coefficients possess the property of simultaneous approximation, that is, they approximate not only the function but also its derivatives. We establish direct estimates of the error of that approximation in uniform norm by means o...

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Bibliographic Details
Published in:	arXiv.org
Main Author:	Draganov, Borislav R
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 07.05.2018
Subjects:	Approximation Mathematical analysis Polynomials Smoothness
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	We prove that several forms of the Bernstein polynomials with integer coefficients possess the property of simultaneous approximation, that is, they approximate not only the function but also its derivatives. We establish direct estimates of the error of that approximation in uniform norm by means of moduli of smoothness. Moreover, we show that the sufficient conditions under which those estimates hold are also necessary.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1804.08248