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.

Motornyi V.P. "Approximation of functions by algebraic polynomials in $$$L_p$$$ metric", Izv. AN sssr. Ser. Matem., 1971; 35(4): pp. 874-899.

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

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

Ul'yanov P.L. "Inclusion of certain classes $$$H_p^{\omega}$$$ of functions", Izv. AN ussr. Ser. Matem., 1968; 32(3): pp. 649-686.




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

  

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