Mean approximation of functions by algebraic polynomials

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


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


мodulus of continuity; Jackson theorem


Lebed' G.K. "Inequalitied 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 the approximation of non-periodic functions by algebraic polynomials", Vestn. Mosk. un-ta, 1960; 4: pp. 14-25. (in Russian)

Potapov M.K. "On the approximation by algebraic polynomials in $$$L_p$$$ metric", Researches on modern problems of constructive function theory, Moscow, 1961. (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)

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)




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