Geodesic
The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials
Sbornik. Mathematics, Tome 204 (2013) no. 12, pp. 1819-1838

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The paper concerns the approximation properties of the Bernstein-Stechkin summability method for trigonometric Fourier series. The Jackson-Stechkin theorem is refined. Moreover, for any continuous periodic function not only is the exact upper estimate for approximation found, a lower estimate of the same order is also put forward. To do this special moduli of smoothness and the $K$-functional are introduced. Bibliography: 16 titles.
Keywords: $B$-spline, modulus of smoothness, $K$-functional, Fourier transform of a measure
Mots-clés : Fourier multiplier. 
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     author = {R. M. Trigub},
     title = {The exact order of approximation to periodic functions by {Bernstein-Stechkin} polynomials},
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R. M. Trigub. The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials. Sbornik. Mathematics, Tome 204 (2013) no. 12, pp. 1819-1838. http://geodesic.mathdoc.fr/item/SM_2013_204_12_a6/