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 Mat. Zametki, 2003, Volume 74, Issue 4, Pages 612–617 (Mi mz295)

Coincidence of Least Uniform Deviations of Functions from Polynomials and Rational Fractions

A. P. Starovoitov

Francisk Skorina Gomel State University

Abstract: For a given nonincreasing vanishing sequence $\{a_n\}^\infty_{n=0}$ of nonnegative real numbers, we find necessary and sufficient conditions for a sequence $\{n_k\}^\infty_{k=0}$ to have the property that for this sequence there exists a function f continuous on the interval $[0,1]$ and satisfying the condition that $R_{n_k,m_k}(f)=E_{n_k}(f)=a_{n_k}$, $k=0,1,2,…$, where $E_n(f)$ and $R_{n,m}(f)$ are the best uniform approximations to the function $f$ by polynomials whose degree does not exceed $n$ and by rational functions of the form $r_{n,m}(x)=p_n(x)/q_m(x)$, respectively.

DOI: https://doi.org/10.4213/mzm295

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English version:
Mathematical Notes, 2003, 74:4, 578–582

Bibliographic databases:

UDC: 517.51

Citation: A. P. Starovoitov, “Coincidence of Least Uniform Deviations of Functions from Polynomials and Rational Fractions”, Mat. Zametki, 74:4 (2003), 612–617; Math. Notes, 74:4 (2003), 578–582

Citation in format AMSBIB
\Bibitem{Sta03} \by A.~P.~Starovoitov \paper Coincidence of Least Uniform Deviations of Functions from Polynomials and Rational Fractions \jour Mat. Zametki \yr 2003 \vol 74 \issue 4 \pages 612--617 \mathnet{http://mi.mathnet.ru/mz295} \crossref{https://doi.org/10.4213/mzm295} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2042974} \zmath{https://zbmath.org/?q=an:1071.41007} \transl \jour Math. Notes \yr 2003 \vol 74 \issue 4 \pages 578--582 \crossref{https://doi.org/10.1023/A:1026108330281} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000186455400032} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0346494621} 

• http://mi.mathnet.ru/eng/mz295
• https://doi.org/10.4213/mzm295
• http://mi.mathnet.ru/eng/mz/v74/i4/p612

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This publication is cited in the following articles:
1. Almira J.M. Oikhberg T., “Approximation Schemes Satisfying Shapiro's Theorem”, J. Approx. Theory, 164:5 (2012), 534–571
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