Geodesic
On Best Polynomial Approximations in $L_2$
Matematičeskie zametki, Tome 70 (2001) no. 3, pp. 334-345

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For the $\boldsymbol\tau$-moduli of smoothness of $m$th order, we calculate exact constants in Jackson-type inequalities. We also obtain the exact values of the $n$-widths of classes of functions whose $r$th derivatives are characterized by $\boldsymbol\tau$-moduli of smoothness majorized by functions satisfying certain constraints. We present an example of the majorant for which all the stated requirements are satisfied. 
@article{MZM_2001_70_3_a1,
     author = {S. B. Vakarchuk},
     title = {On {Best} {Polynomial} {Approximations} in $L_2$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {334--345},
     publisher = {mathdoc},
     volume = {70},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a1/}
}
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S. B. Vakarchuk. On Best Polynomial Approximations in $L_2$. Matematičeskie zametki, Tome 70 (2001) no. 3, pp. 334-345. http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a1/