Exact Values of the Approximations of Differentiable Functions by Poisson-Type Integrals

The asymptotic properties of Poisson-type integrals on the classes of differentiable functions are analyzed using modern methods of the optimal solution theory and approximation theory. Exact values of the upper bound of the deviation of functions of the Sobolev classes from Poisson-type integrals in the uniform metric are found. The research method used in the article makes it possible to estimate the error of the deviation of the classes of differentiable functions from their polyharmonic Poisson integrals with a predetermined accuracy. The results obtained in the study will contribute to the construction of higher-quality mathematical models of natural and social phenomena and, therefore, to more efficient solution of many problems of applied mathematics.