We obtain asymptotic equalities for the least upper bounds of approximations by Zygmund sums in the uniform metric on the classes of continuous 2π-periodic functions whose (ψ, β)-derivatives belong to the set H ω in the case where the sequences ψ that generate the classes tend to zero not faster than a power function.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 4, pp. 524–537, April, 2009.
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Serdyuk, A.S., Ovsii, E.Y. Approximation of the classes C ψβ H ω by generalized Zygmund sums. Ukr Math J 61, 627–644 (2009). https://doi.org/10.1007/s11253-009-0229-6
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DOI: https://doi.org/10.1007/s11253-009-0229-6