On approximation of functions by algebraic polynomials in $$$L^p_{\rho}$$$ metric

S.V. Goncharov (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0002-8071-8746

Abstract


The version has been found, of improved Jackson's theorem analogue, concerning the approximation by algebraic polynomials on the interval in the integral metric for some classes of functions being integrable with the following weight: $$$\rho(x) = (1-x)^{\alpha} (1+x)^{\beta}$$$.

References


Brudnyi Yu.A. "Approximation of functions by algebraic polynomials", Izv. AN SSSR, 1968; 32(4): pp. 780-787. (in Russian) doi:10.1070/IM1968v002n04ABEH000662

Motornyi V.P. "Approximation of functions by algebraic polynomials in $$$L_p$$$ metric", Izv. AN SSSR. Ser.: Matematika, 1971; 35(4): pp. 874-899. (in Russian) doi:10.1070/IM1971v005n04ABEH001122

Potapov M.K. "On theorems of Jackson type in $$$L_p$$$ metric", Dokl. AN SSSR, 1956; 111(6): pp. 1185-1188. (in Russian)

Ul'yanov P.L. "On series by Haar system", Matem. sbornik, 1964; 63(3): pp. 356-391. (in Russian)

Ul'yanov P.L. "Inclusion of certain classes $$$H_p^{\omega}$$$ of functions", Izvestiya AN USSR. Ser. matem., 1968; 32(3): pp. 649-686. (in Russian) doi:10.1070/IM1968v002n03ABEH000650




DOI: https://doi.org/10.15421/240908

  

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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