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

This article is cited in 1 scientific paper (total in 1 paper)

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
Received: 26.04.1999

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
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\paper Coincidence of Least Uniform Deviations of Functions from Polynomials and Rational Fractions
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\vol 74
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\pages 612--617
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\pages 578--582
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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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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