Mean approximation of functions by algebraic polynomials

V.P. Motornyi (Oles Honchar Dnipropetrovsk National University)
M.S. Klimenko (Oles Honchar Dnipropetrovsk National University)

Abstract


Estimates for approximation of functions with given majorant of modulus of continuity by polynomials in integral metrics were estalished.

Keywords


мodulus of continuity; Jackson theorem

References


Lebed' G.K. "Inequalities for polynomials and their derivatives", Dokl. AN SSSR, 1957; 117(4): pp. 570-572. (in Russian)

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

Potapov M.K. Some problems of the best approximation in $$$L_p$$$ metric: Diss. Cand.Phys.-Math.Sc., Moscow, 1956; 105 p. (in Russian)

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

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

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

Brudnyi Yu.A. "Generalization of one theorem of A.F. Timan", Dokl. AN SSSR, 1963; 148(6): pp. 1237-1240. (in Russian)

Motornyi V.P. "On mean convergence of Fourier series by Legendre polynomials", Izv. AN SSSR. Ser. Matematika, 1973; 37: pp. 135-147. (in Russian) doi:10.1070/IM1973v007n01ABEH001929




DOI: https://doi.org/10.15421/241215

  

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Copyright (c) 2012 V.P. Motornyi, M.S. Klimenko

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