Structural characteristics of functions from L_2 and the exact values of widths of some functional classes

摘要

Exact inequalities of the Jackson type are obtained for the averaged characteristic of smoothness of functions that was proposed by K. V. Runovskii. The exact values of some n-widths of classes of differentiable functions defined by the indicated characteristic of smoothness, as well as majorants satisfying the definite conditions, are calculated.