On the value of the widths of some classes of functions from $L_{2}$

In this paper we find sharp inequalities of Jackson-Stechkin type between the best approximations of periodic differentiable functions by trigonometric polynomials and generalized moduli of continuity of $m$-th order in the space $L_{2}.$ The exact values of various $n$-widths of classes of functions from $L_{2}$ defined by the generalized modus of continuity of the $r$-th derivative of the function f are calculated.