A Complete Asymptotic Expansion for Bernstein–Chlodovsky Polynomials for Functions on $$\mathbb {R}$$-Reference-Cited by-同舟云学术

A Complete Asymptotic Expansion for Bernstein–Chlodovsky Polynomials for Functions on $$\mathbb {R}$$

Published:2020-10-30 Issue:6 Volume:17 Page:
ISSN:1660-5446
Container-title:Mediterranean Journal of Mathematics
language:en
Short-container-title:Mediterr. J. Math.

Author:

Abel Ulrich^ORCID,Karsli Harun

Abstract

AbstractWe consider a variant of the Bernstein–Chlodovsky polynomials approximating continuous functions on the entire real line and study its rate of convergence. The main result is a complete asymptotic expansion. As a special case we obtain a Voronovskaja-type formula previously derived by Karsli [11].

Funder

Technische Hochschule Mittelhessen

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.1007/s00009-020-01632-1.pdf

Reference14 articles.

1. Abel, U.: A Voronovskaya-type result for simultaneous approximation by Bernstein–Chlodovsky polynomials, Results Math. 74 (2019): Paper No. 117, 12 p. https://doi.org/10.1007/s00025-019-1036-5

2. Abel, U., Ivan, M.: Asymptotic expansion of the multivariate Bernstein polynomials on a simplex. Approx. Theory Appl. 16, 85–93 (2000)

3. Abel, U., Karsli, H.: Complete Asymptotic Expansions for Bernstein–Chlodovsky Polynomials. In: CONSTRUCTIVE THEORY OF FUNCTIONS, Sozopol 2016 (K. Ivanov, G. Nikolov and R. Uluchev, Eds.), pp. 1–12, Prof. Marin Drinov Academic Publishing House, Sofia, (2017)

4. Abel, U., Karsli, H.: Asymptotic expansions for Bernstein–Durrmeyer–Chlodovsky polynomials. Results Math. 73 (2018): Paper No. 104, 12 p. https://doi.org/10.1007/s00025-018-0863-0

5. Albrycht, J., Radecki, J.: On a generalization of the theorem of Voronovskaya. Zeszyty Naukowe UAM, Zeszyt 2, Poznan, (1960), 1–7

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