Approximation of Periodic Functions of Many Variables in Metric Spaces by Piecewise-Constant Functions - Agoshkova, T. A. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
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.