Geodesic
A Sharp Inequality of Jackson--Stechkin type in~$L_2$ and the Widths of Functional Classes
Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 328-336

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We obtain sharp inequalities of Jackson–Stechkin type in which the modulus of continuity of the function is defined in terms of the Steklov function. For classes of functions given by this characteristic, we obtain sharp values of the $n$-widths.
Keywords: inequality of Jackson–Stechkin type, modulus of continuity, Fourier series, Steklov function, Bernstein $n$-width, Kolmogorov $n$-width, Gelfand $n$-width. 
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     author = {S. B. Vakarchuk and V. I. Zabutnaya},
     title = {A {Sharp} {Inequality} of {Jackson--Stechkin} type in~$L_2$ and the {Widths} of {Functional} {Classes}},
     journal = {Matemati\v{c}eskie zametki},
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     volume = {86},
     number = {3},
     year = {2009},
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S. B. Vakarchuk; V. I. Zabutnaya. A Sharp Inequality of Jackson--Stechkin type in~$L_2$ and the Widths of Functional Classes. Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 328-336. http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a1/