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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 4, Pages 5–17 (Mi timm636)  

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

Direct and inverse theorems in approximation theory for periodic functions in S. B. Stechkins papers and the development of these theorems

V. I. Ivanov

Tula State University

Abstract: S. B. Stechkin made a considerable contribution to an important aspect of approximation theory for periodic functions concerned with direct and inverse theorems. We present the history of development of this research area and pose new problems.

Keywords: best approximation, module of continuity, Jackson–Stechkin inequality, inverse inequality.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 273, suppl. 1, S1–S13

UDC: 517.5
Received: 01.10.2010

Citation: V. I. Ivanov, “Direct and inverse theorems in approximation theory for periodic functions in S. B. Stechkins papers and the development of these theorems”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 5–17; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S1–S13

Citation in format AMSBIB
\Bibitem{Iva10}
\by V.~I.~Ivanov
\paper Direct and inverse theorems in approximation theory for periodic functions in S.\,B.~Stechkins papers and the development of these theorems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 4
\pages 5--17
\mathnet{http://mi.mathnet.ru/timm636}
\elib{http://elibrary.ru/item.asp?id=15318483}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 273
\issue , suppl. 1
\pages S1--S13
\crossref{https://doi.org/10.1134/S0081543811050014}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959197465}


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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. R. M. Trigub, “The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials”, Sb. Math., 204:12 (2013), 1819–1838  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. R. A. Veprintsev, “Otsenka snizu konstanty Dzheksona v prostranstvakh $L_p$ na sfere s vesom Danklya, svyazannym s gruppoi diedra”, Chebyshevskii sb., 16:3 (2015), 95–123  mathnet  elib
    3. Pietsch A., “Traces on Operator Ideals and Related Linear Forms on Sequence Ideals (Part Iv)”, Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics: the Albrecht Bottcher Anniversary Volume, Operator Theory Advances and Applications, 259, eds. Bini D., Ehrhardt T., Karlovich A., Spitkovsky I., Springer International Publishing Ag, 2017, 593–619  crossref  mathscinet  zmath  isi  scopus
    4. Gorbachev D.V., Ivanov V.I., Tikhonov S.Yu., “Positive l-P-Bounded Dunkl-Type Generalized Translation Operator and Its Applications”, Constr. Approx., 49:3 (2019), 555–605  crossref  isi
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