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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 5, Pages 1132–1148 (Mi izv2195)  

This article is cited in 9 scientific papers (total in 9 papers)

On the order of approximation of convex functions by rational functions

A. P. Bulanov


Abstract: We show that for arbitrary convex functions the order of approximation (in the metric $C[a,b]) by rational functions of degree no higher than $n$ does not exceed the quantity $C\cdot M\cdot\frac{\ln^2n}n$ ($C$ an absolute constant, $M$ the maximum modulus of the convex function). We prove also the existence of a convex function whose order of approximation is greater than $\frac1{n\ln^2n}$.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:5, 1067–1080

Bibliographic databases:

UDC: 517.5
MSC: 41A20, 52A41
Received: 20.01.1969

Citation: A. P. Bulanov, “On the order of approximation of convex functions by rational functions”, Izv. Akad. Nauk SSSR Ser. Mat., 33:5 (1969), 1132–1148; Math. USSR-Izv., 3:5 (1969), 1067–1080

Citation in format AMSBIB
\Bibitem{Bul69}
\by A.~P.~Bulanov
\paper On the order of approximation of convex functions by rational functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 5
\pages 1132--1148
\mathnet{http://mi.mathnet.ru/izv2195}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=254470}
\zmath{https://zbmath.org/?q=an:0209.09702|0194.09402}
\transl
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 5
\pages 1067--1080
\crossref{https://doi.org/10.1070/IM1969v003n05ABEH000831}


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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. A. P. Bulanov, “Rational approximations to convex functions with given modulus of continuity”, Math. USSR-Sb., 13:3 (1971), 473–490  mathnet  crossref  mathscinet  zmath
    2. A. A. Abdugapparov, “On rational approximations of functions with a convex derivative”, Math. USSR-Sb., 22:4 (1974), 619–629  mathnet  crossref  mathscinet  zmath
    3. A. Khatamov, “On rational approximations of functions with a convex derivative”, Math. USSR-Sb., 27:2 (1975), 239–250  mathnet  crossref  mathscinet  zmath
    4. V. A. Popov, P. P. Petrushev, “The exact order of the best approximation to convex functions by rational functions”, Math. USSR-Sb., 32:2 (1977), 245–251  mathnet  crossref  mathscinet  zmath  isi
    5. A. P. Bulanov, “Approximation, by rational functions, of convex functions with given modulus of continuity”, Math. USSR-Sb., 34:1 (1978), 1–24  mathnet  crossref  mathscinet  zmath
    6. A.R Reddy, “Recent advances in Chebyshev rational approximation on finite and infinite intervals”, Journal of Approximation Theory, 22:1 (1978), 59  crossref
    7. V. N. Rusak, I. V. Rybachenko, “The Properties of Functions and Approximation by Summation Rational Operators on the Real Axis”, Math. Notes, 76:1 (2004), 103–110  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. V. N. Konovalov, “On the Orders of Nonlinear Approximations for Classes of Functions of Given Form”, Math. Notes, 78:1 (2005), 88–104  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. V. N. Konovalov, “Impact of the shape of functions on the orders of piecewise polynomial and rational approximation”, Sb. Math., 196:5 (2005), 623–648  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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