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Formed in the 1960s, the classical methods of guaranteeing estimation are applied to provide navigation for various modes of transport. Many works of both foreign and domestic authors are devoted to the application of this method. Guaranteed estimation problems are methodologically substantiated by solving extremal problems, in particular, by the theory of optimal recovery of various classes of functions. This paper studies one of such problems, namely, the problem of optimal recovery of higher-order derivatives of functions of the Hardy class H^p,p≥1, given inthe unit circle at zero according to information about their values at the points z_1,…,z_n, forming a regular polygon centered at the origin. Thework consists of an introduction, two main sections, a presentation of the results and a conclusion. In the introduction, we present the necessary notions and results from [7]-[10]. The first section contains the error of the best method for approximating the derivatives f^((N) ) (0),1≤N≤n-1 (f(z)∈H_p ) with respect to the values f(z_1 ),….,f(z_n ). The correspondingextremal functions are also written here. In the second, the coefficients of the linear best approximation method are calculated. Examples of the optimal recovery of the first derivative of functions of the Hardy class H_H_p,p≥1 at zero from their values at a given finite number of pointsforming a regular polygon centered at the point (0,0) are given.

In the below work the problem of optimal recovery of functions in Hardy class is covered. Namely, by the values ​​of these functions in a finite number of points lying in the unit circle determined their value at a given point. Coefficients of the linear best approximation method and error of the best method are calculated. The functions are considered with some given weight function.

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