Geodesic
Some inequalities between the best polynomial approximation and averaged finite-difference norms in space $L_2$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2021), pp. 78-91

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Exact constants are found in inequalities type Jackson-Stechkin for smoothness characte-ristics $\Lambda_{m}(f), m \in\mathbb{N} $ determined by averaging the norm in $L_{2}$ of finite differences of the $m$-th order of the functions $f$. For function classes, defined by the smoothness characteristic $\Lambda_{m}(f)$, and the majorant $\Phi $ satisfying a certain condition, calculated the exact values of different $n$-widths.
Keywords: best approximations, finite differences of the $m$-th order, smoothness characteristic, $n$-widths. 
@article{IVM_2021_10_a6,
     author = {M. Sh. Shabozov and M. A. Abdulkhaminov},
     title = {Some inequalities between the best polynomial approximation and averaged finite-difference norms in space $L_2$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {78--91},
     publisher = {mathdoc},
     number = {10},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_10_a6/}
}
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M. Sh. Shabozov; M. A. Abdulkhaminov. Some inequalities between the best polynomial approximation and averaged finite-difference norms in space $L_2$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2021), pp. 78-91. http://geodesic.mathdoc.fr/item/IVM_2021_10_a6/