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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 2, Pages 423–434 (Mi izv2303)  

This article is cited in 7 scientific papers (total in 7 papers)

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

N. P. Korneichuk


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 $W^rH_\omega$ by functions of the class $W^{r+1}K$.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:2, 417–428

Bibliographic databases:

UDC: 517.5
MSC: 41A30, 42A04
Received: 19.08.1971

Citation: N. P. Korneichuk, “Inequalities for differentiable periodic functions and best approximation of one class of functions by another”, Izv. Akad. Nauk SSSR Ser. Mat., 36:2 (1972), 423–434; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 2
\pages 423--434
\mathnet{http://mi.mathnet.ru/izv2303}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=318738}
\zmath{https://zbmath.org/?q=an:0281.41004}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 2
\pages 417--428
\crossref{https://doi.org/10.1070/IM1972v006n02ABEH001880}


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

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  zmath
    2. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. 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  mathnet  crossref  mathscinet  zmath  isi
    5. S. N. Kudryavtsev, “Approximating one class of finitely differentiable functions by another”, Izv. Math., 61:2 (1997), 347–362  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. S. K. Bagdasarov, “Maximization of functionals in $H^\omega [a,b]$”, Sb. Math., 189:2 (1998), 159–226  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. N. P. Korneichuk, “Best Approximation and Symmetric Decreasing Rearrangements of Functions”, Proc. Steklov Inst. Math., 232 (2001), 172–186  mathnet  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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