Exact Constants in Kolmogorov-Type Inequalities

M. I. Zelikin ; L. F. Zelikina

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

Résumé

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.

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