Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Tyuleneva A. A. Approximation of the Riemann–Liouville Integrals by Algebraic Polynomials on the Segment. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 3, pp. 305-311. DOI: 10.18500/1816-9791-2014-14-3-305-311, EDN: SMSJWF

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
10.09.2014
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.51
DOI: 
10.18500/1816-9791-2014-14-3-305-311
EDN: 
SMSJWF

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

Autors: 
Tyuleneva Anna Anotol'evna, Saratov State University
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 ε-entropy of the image of a Hölder type class under Riemann–Liouville integration operator.

Key words: 
p-variation metric
Lp space
Riemann–Liouville integral
best approximation
algebraic polynomials
ε-entropy
References: 
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Received: 
19.03.2014
Accepted: 
23.07.2014
Published: 
10.09.2014
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