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Approximation to Functions from the Classes of ψ-Integrals by the Zygmund Sums

Abstract In this paper we investigate the approximation by the Zygmund sums in a given class of certain functions. Especially, we get asymptotic formulas which the Kolmogorov-Nikol’skii problem is solved in a given metric of the certain space for the given class of functions which satisfy the various conditions, i.e. asymptotic formulas for the value En(C ∞, Z n)C = sup f∈C ∞ ‖f(x) − Z n(f ;x)‖C ,