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Mat. Zametki, 1973, Volume 13, Issue 3, Pages 457–468 (Mi mz7144)  

On the order of an approximation of functions on sets of positive measure by linear positive polynomial operators

R. K. Vasil'ev

First Moscow Institute of Medicine

Abstract: It is proved that at almost all points the order of approximation, even of one of the functions 1, $\cos x$, $\sin x$ by means of a sequence of linear positive polynomial operators having uniformly bounded norms, is not higher than $1/n^2$. Refinements of this result are given for operators of convolution type.

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English version:
Mathematical Notes, 1973, 13:3, 274–280

Bibliographic databases:

UDC: 517.5
Received: 30.12.1971

Citation: R. K. Vasil'ev, “On the order of an approximation of functions on sets of positive measure by linear positive polynomial operators”, Mat. Zametki, 13:3 (1973), 457–468; Math. Notes, 13:3 (1973), 274–280

Citation in format AMSBIB
\Bibitem{Vas73}
\by R.~K.~Vasil'ev
\paper On the order of an~approximation of functions on sets of positive measure by linear positive polynomial operators
\jour Mat. Zametki
\yr 1973
\vol 13
\issue 3
\pages 457--468
\mathnet{http://mi.mathnet.ru/mz7144}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=322406}
\zmath{https://zbmath.org/?q=an:0275.41009}
\transl
\jour Math. Notes
\yr 1973
\vol 13
\issue 3
\pages 274--280
\crossref{https://doi.org/10.1007/BF01155672}


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