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Mat. Zametki, 1976, Volume 19, Issue 1, Pages 11–17 (Mi mz7718)  

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

Upper bounds for the best one-sided approximation by splines of the classes $W^rL_1$

V. G. Doronina, A. A. Ligunb

a Dnepropetrovsk State University
b Dneprodzerzhinsk Industrial Institute

Abstract: In the present note we will investigate the problem of the one-sided approximation of functions by $n$-dimensional subspaces. In particular, we will find the exact value of the best one-sided approximation of the class $W^rL_1$ ($r=1,2,…$) of all periodic functions $f(x)$ of period $2\pi$ for which $f^{(r-1)}(x)$ ($f^{(0)}(x)=f(x)$) is absolutely continuous and $\|f^{(r)}\|_{L_1}\le1$ by periodic spline functions $S_{2n,\mu}$ ($\mu=0,1,…$, $n=1,2,…$) of period $2\pi$, order $\mu$, and deficiency 1.

Full text: PDF file (424 kB)

English version:
Mathematical Notes, 1976, 19:1, 7–10

Bibliographic databases:

UDC: 517.5
Received: 25.12.1974

Citation: V. G. Doronin, A. A. Ligun, “Upper bounds for the best one-sided approximation by splines of the classes $W^rL_1$”, Mat. Zametki, 19:1 (1976), 11–17; Math. Notes, 19:1 (1976), 7–10

Citation in format AMSBIB
\Bibitem{DorLig76}
\by V.~G.~Doronin, A.~A.~Ligun
\paper Upper bounds for the best one-sided approximation by splines of the classes $W^rL_1$
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 1
\pages 11--17
\mathnet{http://mi.mathnet.ru/mz7718}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=412680}
\zmath{https://zbmath.org/?q=an:0352.41026|0324.41017}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 1
\pages 7--10
\crossref{https://doi.org/10.1007/BF01147610}


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    This publication is cited in the following articles:
    1. Babenko V.F., Parfinovich N.V., “NONSYMMETRIC APPROXIMATIONS OF CLASSES OF PERIODIC FUNCTIONS BY SPLINES OF DEFECT 2 AND JACKSON-TYPE INEQUALITIES”, Ukrainian Math J, 61:11 (2009), 1695–1709  crossref  isi
  • Математические заметки Mathematical Notes
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