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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2021, Issue 4(49), Pages 92–94
DOI: https://doi.org/10.54341/20778708_2021_4_49_92
(Mi pfmt816)
 

MATHEMATICS

Direct and inverse theorems of approximation theory for the generalized modulus of smoothness of some class of functions

G. N. Kazimirov

Francisk Skorina Gomel State University
References:
Abstract: This article proves the coincidence of generalized moduli of smoothness of the $k$-s order, defined with the help of Gegenbauers generalized shift operator, with different and identical shifts and, as a consequence, direct and inverse theorems of approximation theory by algebraic polynomials are obtained.
Keywords: the best approximation by algebraic polynomials, Gegenbauers generalized shift operator, generalized modulus of smoothness.
Received: 28.06.2021
Document Type: Article
UDC: 517.5
Language: Russian
Citation: G. N. Kazimirov, “Direct and inverse theorems of approximation theory for the generalized modulus of smoothness of some class of functions”, PFMT, 2021, no. 4(49), 92–94
Citation in format AMSBIB
\Bibitem{Kaz21}
\by G.~N.~Kazimirov
\paper Direct and inverse theorems of approximation theory for the generalized modulus of smoothness of some class of functions
\jour PFMT
\yr 2021
\issue 4(49)
\pages 92--94
\mathnet{http://mi.mathnet.ru/pfmt816}
\crossref{https://doi.org/10.54341/20778708_2021_4_49_92}
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