Cite this article as:

Tyuleneva A. A. Approximation of the Riemann–Liouville Integrals by Algebraic Polynomials on the Segment . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 3, pp. 305-311. DOI: https://doi.org/10.18500/1816-9791-2014-14-3-305-311

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.51

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

Authors: 
Tyuleneva Anna Anotol'evna, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , aatuleneva@km.ru
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.
DOI: 
https://doi.org/10.18500/1816-9791-2014-14-3-305-311
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