We prove the direct and inverse Jackson- and Bernstein-type theorems for averaged approximations of periodic functions of many variables by piecewise-constant functions with uniform partition of the period torus in metric spaces with integral metric given by a function ψ of the type of modulus of continuity.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 10, pp. 1303–1314, June, 2013.
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Agoshkova, T.A. Approximation of Periodic Functions of Many Variables in Metric Spaces by Piecewise-Constant Functions. Ukr Math J 65, 1447–1459 (2014). https://doi.org/10.1007/s11253-014-0871-5
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DOI: https://doi.org/10.1007/s11253-014-0871-5