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Mat. Zametki, 1971, Volume 9, Issue 4, Pages 441–447 (Mi mz7028)  

This article is cited in 3 scientific papers (total in 3 papers)

Algebraic-polynomial approximation of functions satisfying a Lipschitz condition

N. P. Korneichuka, A. I. Polovinab

a Dnepropetrovsk State University
b Kommunarskii Mining and Metallurgical Institute

Abstract: For functions $f(x)\in KH^{(\alpha)}$ (satisfying the Lipschitz condition of order $\alpha$ ($0<\alpha<1$) with constant $K$ on $[-1, 1]$), the existence is proved of a sequence $P_n(f; x)$ of algebraic polynomials of degree $n=1, 2, …$, such that $|f(x)-P_{n-1}(f; x)|\leqslant\sup\limits_{f\in KH^{(\alpha)}}E_n(f)[(1-x^2)^{\alpha/2}+o(1)]$ when $n\to\infty$, uniformly for $x\in[-1, 1]$ , where $E_n(f)$ is the best approximation of $f(x)$ by polynomials of degree not higher than $n$.

Full text: PDF file (479 kB)

English version:
Mathematical Notes, 1971, 9:4, 254–257

Bibliographic databases:

UDC: 517.5
Received: 18.03.1970

Citation: N. P. Korneichuk, A. I. Polovina, “Algebraic-polynomial approximation of functions satisfying a Lipschitz condition”, Mat. Zametki, 9:4 (1971), 441–447; Math. Notes, 9:4 (1971), 254–257

Citation in format AMSBIB
\Bibitem{KorPol71}
\by N.~P.~Korneichuk, A.~I.~Polovina
\paper Algebraic-polynomial approximation of functions satisfying a~Lipschitz condition
\jour Mat. Zametki
\yr 1971
\vol 9
\issue 4
\pages 441--447
\mathnet{http://mi.mathnet.ru/mz7028}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=287238}
\zmath{https://zbmath.org/?q=an:0226.41002|0216.38902}
\transl
\jour Math. Notes
\yr 1971
\vol 9
\issue 4
\pages 254--257
\crossref{https://doi.org/10.1007/BF01387776}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. P. Motornyi, “Approximation of a Class of Singular Integrals by Algebraic Polynomials with Regard to the Location of a Point on an Interval”, Proc. Steklov Inst. Math., 232 (2001), 260–277  mathnet  mathscinet  zmath
    3. A. V. Mironenko, “On the Jackson–Stechkin inequality for algebraic polynomials”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S116–S123  mathnet  crossref  isi  elib
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