Geodesic
Exact Constants in Kolmogorov-Type Inequalities
Informatics and Automation, Investigations in the theory of differentiable functions of many variables and its applications. Part 18, Tome 227 (1999), pp. 137-145

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This work is concerned with the evaluation of Kolmogorov constants. We suggest an effective algorithm using the chattering-control theory for approximately evaluating the best constants $K_m$ in a series of Kolmogorov-type inequalities, which has not been studied so far. The best Kolmogorov constant $K_3$ is found, and asymptotic estimates of $K_m$ with large $m$ are obtained. 
@article{TRSPY_1999_227_a8,
     author = {M. I. Zelikin and L. F. Zelikina},
     title = {Exact {Constants} in {Kolmogorov-Type} {Inequalities}},
     journal = {Informatics and Automation},
     pages = {137--145},
     publisher = {mathdoc},
     volume = {227},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_1999_227_a8/}
}
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M. I. Zelikin; L. F. Zelikina. Exact Constants in Kolmogorov-Type Inequalities. Informatics and Automation, Investigations in the theory of differentiable functions of many variables and its applications. Part 18, Tome 227 (1999), pp. 137-145. http://geodesic.mathdoc.fr/item/TRSPY_1999_227_a8/