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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, Volume 14, Issue 3, Pages 305–311 (Mi isu514)  

Mathematics

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

A. A. Tyleneva

Saratov State University named after N. G. Chernyshevsky

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.

DOI: https://doi.org/10.18500/1816-9791-2014-14-3-305-311

Full text: PDF file (176 kB)
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Bibliographic databases:

UDC: 517.51

Citation: A. A. Tyleneva, “Approximation of the Riemann–Liouville Integrals by Algebraic Polynomials on the Segment”, Izv. Saratov Univ. (N.S.), Ser. 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. (N.S.), Ser. 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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