V. F. Storchai, “The deviation of polygonal functions in the $L_p$ metric”, Mat. Zametki, 5:1 (1969), 31–37; Math. Notes, 5:1 (1969), 21

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Matematicheskie Zametki, 1969, Volume 5, Issue 1, Pages 31–37 (Mi mzm6804)

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

The deviation of polygonal functions in the $L_p$ metric

V. F. Storchai

Dnepropetrovsk State University

Full-text PDF (344 kB) Citations (8)

Abstract: The precise value is given of the upper bound of the deviation in the $L_p$ metric $(1\le p<\infty)$ of a function $f(x)$ in the class $H_\omega$, given by a convex modulus of continuity $\omega(t)$, from its polygonal approximation at the points $x_k=k/n$ ($k=0,1,\dots,n$).

Received: 19.01.1968

English version:
Mathematical Notes, 1969, Volume 5, Issue 1, Pages 21–25
DOI: https://doi.org/10.1007/BF01098710

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: V. F. Storchai, “The deviation of polygonal functions in the $L_p$ metric”, Mat. Zametki, 5:1 (1969), 31–37; Math. Notes, 5:1 (1969), 21–25

Citation in format AMSBIB

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\by V.~F.~Storchai

\paper The deviation of polygonal functions in the $L_p$ metric

\jour Mat. Zametki

\yr 1969

\vol 5

\issue 1

\pages 31--37

\mathnet{http://mi.mathnet.ru/mzm6804}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=239331}

\zmath{https://zbmath.org/?q=an:0177.08802}

\transl

\jour Math. Notes

\yr 1969

\vol 5

\issue 1

\pages 21--25

\crossref{https://doi.org/10.1007/BF01098710}

Linking options:

https://www.mathnet.ru/eng/mzm6804

https://www.mathnet.ru/eng/mzm/v5/i1/p31

This publication is cited in the following 8 articles:

A. A. Shabozova, “Approximation of Curves by Broken Lines in Lp”, Vestnik St.Petersb. Univ.Math., 57:4 (2024), 548
A. A. Shabozova, “Priblizhenie prostranstvennykh krivykh lomanymi v $L_{p}$”, Tr. IMM UrO RAN, 23, no. 4, 2017, 311–318
Xu, GQ, “The relative n-widths of Sobolev classes with restrictions”, Journal of Approximation Theory, 157:1 (2009), 19
V. L. Velikin, N. A. Nazarenko, “Studies on extremal problems of spline-approximation”, Ukr Math J, 42:1 (1990), 28
N. P. Korneichuk, “Widths in $L_p$ of classes of continuous and of differentiable functions, and optimal methods of coding and recovering functions and their derivatives”, Math. USSR-Izv., 18:2 (1982), 227–247
V. T. Martynyuk, “Approximation by polygonal lines of curves given by parametric equations in the Hausdorff metric”, Ukr Math J, 28:1 (1976), 68
V. L. Velikin, “Precise approximation values by Hermitian splines on classes of differentiable function”, Math. USSR-Izv., 7:1 (1973), 163–184
V. T. Martynyuk, V. F. Storchai, “Approximation by polyhedral functions in a hausdorff metric”, Ukr Math J, 25:1 (1973), 98

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

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