On constants in the Jackson--Stechkin theorem in the case of approximation by algebraic polynomials
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 26-38
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New estimates are proved for the constants $J(k,\alpha )$ in the classical Jackson–Stechkin inequality $E_{n-1}(f) \le J(k, \alpha ) \omega _k (f,{\alpha \pi }/{n})$, $\alpha >0$, in the case of approximation of functions $f \in C[-1,1]$ by algebraic polynomials. The main result of the paper implies the following two-sided estimates for the constants: $1/2\le J(2k,\alpha )10$, $n \ge 2k(2k-1)$, $\alpha \ge 2$.
@article{TM_2018_303_a2,
author = {A. G. Babenko and Yu. V. Kryakin},
title = {On constants in the {Jackson--Stechkin} theorem in the case of approximation by algebraic polynomials},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {26--38},
publisher = {mathdoc},
volume = {303},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TM_2018_303_a2/}
}
TY - JOUR AU - A. G. Babenko AU - Yu. V. Kryakin TI - On constants in the Jackson--Stechkin theorem in the case of approximation by algebraic polynomials JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 2018 SP - 26 EP - 38 VL - 303 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TM_2018_303_a2/ LA - ru ID - TM_2018_303_a2 ER -
%0 Journal Article %A A. G. Babenko %A Yu. V. Kryakin %T On constants in the Jackson--Stechkin theorem in the case of approximation by algebraic polynomials %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 2018 %P 26-38 %V 303 %I mathdoc %U http://geodesic.mathdoc.fr/item/TM_2018_303_a2/ %G ru %F TM_2018_303_a2
A. G. Babenko; Yu. V. Kryakin. On constants in the Jackson--Stechkin theorem in the case of approximation by algebraic polynomials. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 26-38. http://geodesic.mathdoc.fr/item/TM_2018_303_a2/