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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 $R_{n_k,m_k}(f)=E_{n_k}(f)=a_{n_k}$, $k=0,1,2,\dots$, 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.
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
Linking options:
https://www.mathnet.ru/eng/mzm295https://doi.org/10.4213/mzm295 https://www.mathnet.ru/eng/mzm/v74/i4/p612
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Abstract page: | 277 | Full-text PDF : | 178 | References: | 53 | First page: | 1 |
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