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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, Volume 14, Issue 3, Pages 305–311
DOI: https://doi.org/10.18500/1816-9791-2014-14-3-305-311 (Mi isu514) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Approximation of the Riemann–Liouville Integrals by Algebraic Polynomials on the Segment

A. A. Tyleneva

Saratov State University named after N. G. Chernyshevsky
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DOI: https://doi.org/10.18500/1816-9791-2014-14-3-305-311
Abstract: The direct approximation theorem by algebraic polynomials is proved for Riemann–Liouville integrals of order $r>0$. As a corollary, we obtain asymptotic equalities for $\varepsilon$-entropy of the image of a Hölder type class under Riemann–Liouville integration operator.
Key words: $p$-variation metric, $L^p$ space, Riemann–Liouville integral, best approximation, algebraic polynomials, $\varepsilon$-entropy.
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: A. A. Tyleneva, “Approximation of the Riemann–Liouville Integrals by Algebraic Polynomials on the Segment”, Izv. Saratov Univ. Math. Mech. Inform., 14:3 (2014), 305–311
Citation in format AMSBIB
\Bibitem{Tyu14}
\by A.~A.~Tyleneva
\paper Approximation of the Riemann--Liouville Integrals by Algebraic Polynomials on the Segment
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 3
\pages 305--311
\mathnet{http://mi.mathnet.ru/isu514}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-3-305-311}
\elib{https://elibrary.ru/item.asp?id=21967151}
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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