N. P. Korneichuk, “Inequalities for differentiable periodic functions and best approximation of one class of functions by another”, Math. USSR-Izv., 6:2 (1972), 417

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Mathematics of the USSR-Izvestiya, 1972, Volume 6, Issue 2, Pages 417–428
DOI: https://doi.org/10.1070/IM1972v006n02ABEH001880 (Mi im2303)

This article is cited in 8 scientific papers (total in 8 papers)

Inequalities for differentiable periodic functions and best approximation of one class of functions by another

N. P. Korneichuk

English version PDF (509 kB) Citations (8) Russian version article

References:

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DOI: https://doi.org/10.1070/IM1972v006n02ABEH001880

Abstract: New results are obtained in this paper which elucidate properties of differentiable periodic functions connected with rearrangements. These results are applied in order to obtain a sharp estimate of the best uniform approximation of functions of the class

W^{r} H_{ω}

$W^rH_\omega$ by functions of the class

W^{r + 1} K

$W^{r+1}K$ .

Received: 19.08.1971

Bibliographic databases:

UDC: 517.5

MSC: 41A30, 42A04

Language: English

Original paper language: Russian

Citation: N. P. Korneichuk, “Inequalities for differentiable periodic functions and best approximation of one class of functions by another”, Math. USSR-Izv., 6:2 (1972), 417–428

Citation in format AMSBIB

\Bibitem{Kor72}

\by N.~P.~Korneichuk

\paper Inequalities for differentiable periodic functions and best approximation of one class of functions by another

\jour Math. USSR-Izv.

\yr 1972

\vol 6

\issue 2

\pages 417--428

\mathnet{http://mi.mathnet.ru/eng/im2303}

\crossref{https://doi.org/10.1070/IM1972v006n02ABEH001880}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=318738}

\zmath{https://zbmath.org/?q=an:0281.41004}

Linking options:

https://www.mathnet.ru/eng/im2303

https://doi.org/10.1070/IM1972v006n02ABEH001880

https://www.mathnet.ru/eng/im/v36/i2/p423

This publication is cited in the following 8 articles:

Yongping Liu, Man Lu, “Approximation problems on the smoothness classes”, Acta Math Sci, 44:5 (2024), 1721
N. P. Korneichuk, “Best Approximation and Symmetric Decreasing Rearrangements of Functions”, Proc. Steklov Inst. Math., 232 (2001), 172–186
S. K. Bagdasarov, “Maximization of functionals in $H^\omega [a,b]$ ”, Sb. Math., 189:2 (1998), 159–226
S. N. Kudryavtsev, “Approximating one class of finitely differentiable functions by another”, Izv. Math., 61:2 (1997), 347–362
V. T. Shevaldin, “Lower estimates of the widths of the classes of functions defined by a modulus of continuity”, Russian Acad. Sci. Izv. Math., 45:2 (1995), 399–415
S. N. Kudryavtsev, “Some problems in approximation theory for a class of functions of finite smoothness”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 145–164
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
V. P. Motornyi, “On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions”, Math. USSR-Izv., 8:3 (1974), 591–620

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

Известия Академии наук СССР. Серия математическая

Statistics & downloads:
Abstract page:	384
Russian version PDF:	150
English version PDF:	27
References:	79
First page:	1

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