“…At present, the extremal problems of the approximation theory, being related to the study of the approximation properties of linear methods for summing Fourier series, become increasingly relevant in applied mathematics, in particular, in the creation of mathematical models [15][16][17][18][19], in signal transmission [20,21], in the decision theory [22] and others. The problem considered in the paper, as well as those close to it [23][24][25] find practical application in the issues of coding, transmission and reproduction of images.…”