Approximation Properties of the Generalized Abel-Poisson Integrals on the Weyl-Nagy Classes

Abstract

Asymptotic equalities are obtained for the least upper bounds of approximations of functions from the classes Wβ,∞r by the generalized Abel-Poisson integrals Pγ(δ),0γ≤2, for the case r>γ in the uniform metric, which provide the solution to the Kolmogorov–Nikol’skii problem for the given method of approximation on the Weyl-Nagy classes.

Keywords

• Weyl-Nagy classes
• generalized Abel-Poisson integral
• asymptotic equality
• Kolmogorov–Nikol’skii problem
• uniform metric