| Summary: | Asymptotic equalities are obtained for the least upper bounds of approximations of functions from the classes <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>W</mi><mrow><mi>β</mi><mo>,</mo><mo>∞</mo></mrow><mi>r</mi></msubsup></semantics></math></inline-formula> by the generalized Abel-Poisson integrals <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mi>γ</mi></msub><mrow><mo>(</mo><mi>δ</mi><mo>)</mo></mrow><mo>,</mo><mspace width="4pt"></mspace><mn>0</mn><mo><</mo><mi>γ</mi><mo>≤</mo><mn>2</mn><mo>,</mo></mrow></semantics></math></inline-formula> for the case <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>></mo><mi>γ</mi></mrow></semantics></math></inline-formula> 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.
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