Approximation of some classes of periodic functions of many variables

Abstract

We obtain the exact order of deviations of Fejér sums on the class of continuous functions. This order is determined by a given majorant of the best approximations.In the present paper, we establish the order of decrease of the least upper bound of deviations of Fejér sums on the classes of 2π-periodic functions of many variables determined by restrictions imposed on the sequence of the best approximations. In particular, we generalize a one-dimensional result of Stechkin to the case of functions of many variables.Consider the space C T d