Widths in L2 of classes of differentiable functions,defined by higher-order moduli of continuity

Sharp inequalities are obtained in the space L₂, connecting the best approximations of differentiable 2-periodic functions by trigonometric polynomials with integrals containing the higher-order moduli of continuity of the derivatives of these functions. The Kolmogorov widths of certain classes of functions, defined by these moduli of continuity, are computed.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 125–129, January, 1991.