The best approximation of periodic differentiated functions and sharp values of widths of some classes of the function in <i>L</i><sub>2</sub>
The sharp inequalities of Jackson-Stechkin type for the averaged with the weight of moduli of continuity of m -th order were obtained. For the classes of functions determined by majorant and averaged magnitudes, the sharp values of n -widths satisfying stated constrains on majorant, were calculated.