Exact Constants in Kolmogorov-Type Inequalities

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.