Approximation of Periodic Functions of Many Variables in Metric Spaces by Piecewise-Constant Functions
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.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 10, pp 1447-1459.
Citation Example: Agoshkova T. A. Approximation of Periodic Functions of Many Variables in Metric Spaces by Piecewise-Constant Functions // Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1303–1314.