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

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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. 
@article{ISU_2015_15_3_a1,
     author = {S. S. Volosivets and T. V. Likhacheva},
     title = {Several questions of approximation by polynomials with respect to multiplicative systems in weighted $L^p$ spaces},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {251--258},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2015_15_3_a1/}
}
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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/