Geodesic
Approximation of the Riemann--Liouville Integrals by Algebraic Polynomials on the Segment
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 305-311

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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. 
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A. A. Tyleneva. Approximation of the Riemann--Liouville Integrals by Algebraic Polynomials on the Segment. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 305-311. http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a8/