The aim of the article is to establish the form of nonnegative polynomials $y(x)$ of a power which does not exceed the given one, limiting the integral
where $p(x)$ is the given summed function, if the coefficients of the polynomial $y(x)$ satisfy any number s of linear relationships.
Citation Example:Grigoreva I. A. On the application of the Chebyshev-Bernstein method to a class of extremal functions satisfying some relationships, linear with respect to the coefficients // Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 283-291.