Zhyhallo K. M.

UDC 517.5
We obtain the exact equality for the upper bounds of deviations of biharmonic Poisson operators on the Hölder classes of functions continuous on the segment $[-1;1]$.

We establish asymptotic expansions for the values of approximation of functions from the H¨older class by biharmonic Poisson integrals in the uniform and integral metrics.

We solve the Kolmogorov – Nikol’skii problem for biharmonic Poisson integrals on the classes of (ψ, β)- differentiable periodic functions of low smoothness in the uniform metric.

Asymptotic equalities are obtained for upper bounds of deviations of biharmonic Poisson integrals on the classes of $(\psi, \beta)$-differentiable periodic functions in the uniform metric.

We determine the exact values of upper bounds of approximations by biharmonic Poisson integrals on classes of conjugate differentiable functions in uniform and integral metrics.

We obtain the exact values of upper bounds of approximations of classes of periodic conjugate differentiable functions by their Abel–Poisson integrals in uniform and integral metrics.

We determine the exact values and asymptotic decompositions of upper bounds of approximations by biharmonic Poisson integrals on classes of periodic differentiable functions.

On a class of differentiable functions W ^r and the class \(\overline W ^r \) of functions conjugate to them, we obtain a complete asymptotic expansion of the upper bounds \(\mathcal{E}(\mathfrak{N},A\rho )_C \) of deviations of the harmonic Poisson integrals of the functions considered.

We determine the exact value of the upper bound for the deviation of the triharmonic Poisson integral from functions of the Hölder class.

We determine the exact value of the upper bound of the deviation of biharmonic Poisson integrals from functions of the Hölder class.