Geodesic
Several questions of approximation by polynomials with respect to multiplicative systems in weighted $L^p$ spaces
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 251-258 
S. S. Volosivets; T. V. Likhacheva. Several questions of approximation by polynomials with respect to multiplicative systems in weighted $L^p$ spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 251-258. http://geodesic.mathdoc.fr/item/ISU_2015_15_3_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study approximation by Vilenkin polynomials in weighted $L^p$ spaces. We prove the Butzer–Scherer type result on equivalence between the rate of best approximation of a function $f$ and the growth of generalized derivatives and approximating properties of the best approximation polynomial $t_n(f)$. Some applications to the approximation by linear means of the Fourier–Vilenkin series are given.

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