On the best approximation of functions of $n$ variables
We propose a new approach to the solution of the problem of the best approximation, by a certain subspace for functions ofn variables determined by restrictions imposed on the modulus of, continuity of certain partial derivatives. This approach is based on the duality theorem and on the representation of a function as a countable sum of simple functions.
English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 10, pp 1525-1533.
Citation Example: Korneichuk N. P. On the best approximation of functions of $n$ variables // Ukr. Mat. Zh. - 1999. - 51, № 10. - pp. 1352–1359.