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Mat. Zametki, 2009, Volume 85, Issue 4, Pages 538–551 (Mi mz4617)  

This article is cited in 4 scientific papers (total in 4 papers)

Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency 2

V. F. Babenkoab, N. V. Parfinovichb

a Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
b Dnepropetrovsk National University

Abstract: We obtain exact values of best $L_1$-approximations for the classes $W^rF$, $r\in\mathbb N$, of periodic functions whose $r$th derivative belongs to a given rearrangement-invariant set $F$ as well as for the classes $W^rH^\omega$ of periodic functions whose $r$th derivative has a given convex (up) majorant $\omega(t)$ of the modulus of continuity by subspaces of polynomial splines of order $m\ge r+1$ of deficiency 2 with nodes at the points $2k\pi/n$, $n\in\mathbb N$, $k\in\mathbb Z$. It is shown that these subspaces are extremal for the Kolmogorov widths of the corresponding function classes.

Keywords: periodic function, best $L_1$-approximation, periodic function, polynomial spline of deficiency 2, Kolmogorov width, rearrangement-invariant set, modulus of continuity

DOI: https://doi.org/10.4213/mzm4617

Full text: PDF file (569 kB)
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English version:
Mathematical Notes, 2009, 85:4, 515–527

Bibliographic databases:

UDC: 517
Received: 07.03.2008

Citation: V. F. Babenko, N. V. Parfinovich, “Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency 2”, Mat. Zametki, 85:4 (2009), 538–551; Math. Notes, 85:4 (2009), 515–527

Citation in format AMSBIB
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\by V.~F.~Babenko, N.~V.~Parfinovich
\paper Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency~2
\jour Mat. Zametki
\yr 2009
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\issue 4
\pages 538--551
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\pages 515--527
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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathscinet  zmath  isi  scopus
    2. V. F. Babenko, N. V. Parfinovich, “On the Exact Values of the Best Approximations of Classes of Differentiable Periodic Functions by Splines”, Math. Notes, 87:5 (2010), 623–635  mathnet  crossref  crossref  mathscinet  isi
    3. Vasil'eva A.A., “Widths of Weighted Sobolev Classes With Constraints F(a) = Center Dot Center Dot Center Dot = F(K-1)(a) = F(K)(B) = Center Dot Center Dot Center Dot = F(R-1)(B)=0 and the Spectra of Nonlinear Differential Equations”, Russ. J. Math. Phys., 24:3 (2017), 376–398  crossref  mathscinet  zmath  isi  scopus
    4. Parfinovych N.V., “Exact Values of the Best (Oe > 1/4, Beta)-Approximations For the Classes of Convolutions With Kernels That Do Not Increase the Number of Sign Changes”, Ukr. Math. J., 69:8 (2018), 1248–1261  crossref  mathscinet  isi  scopus
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