Geodesic
Sharpening of the estimates for relative widths of classes of differentiable functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 242-253

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We improve the earlier obtained upper estimates for the least value of the coefficient $M$ for which the Kolmogorov widths $d_n(W_C^r,C)$ of the function class $W_C^r$ are equal to the relative widths $K_n(W_C^r,MW_C^j,C)$ of the class $W_C^r$ with respect to the class $MW_C^j$, $j$. 
@article{TM_2010_269_a19,
     author = {Yu. N. Subbotin and S. A. Telyakovskii},
     title = {Sharpening of the estimates for relative widths of classes of differentiable functions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {242--253},
     publisher = {mathdoc},
     volume = {269},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_269_a19/}
}
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Yu. N. Subbotin; S. A. Telyakovskii. Sharpening of the estimates for relative widths of classes of differentiable functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 242-253. http://geodesic.mathdoc.fr/item/TM_2010_269_a19/