Geodesic
Jackson\,--\,Stechkin Inequality and Values of Widths of Some Classes
Dalʹnevostočnyj matematičeskij žurnal, Tome 22 (2022) no. 1, pp. 125-137

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The sharp values of extremal characteristic of special form for classes $L_{2}^{(r)}$, $(r\in\mathbb{Z}_{+})$ containing not only averaged module of continuity but also the averaged with weight $u(t-u)/t$, $0\le u\le t$ of given modulus continuity is calculated. The obtained result is the spreading of well-known S.B. Vakarchuk theorem about averaged module of continuity. For the given characteristic of smoothness, is given an application for the solution of one extremal problem and the values of $n$-widths for some classes of functions in $L_2$ is calculated. 
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     author = {M. Sh. Shabozov and K. K. Palavonov},
     title = {Jackson\,--\,Stechkin {Inequality} and {Values} of {Widths} of {Some} {Classes}},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {125--137},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2022_22_1_a12/}
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M. Sh. Shabozov; K. K. Palavonov. Jackson\,--\,Stechkin Inequality and Values of Widths of Some Classes. Dalʹnevostočnyj matematičeskij žurnal, Tome 22 (2022) no. 1, pp. 125-137. http://geodesic.mathdoc.fr/item/DVMG_2022_22_1_a12/