Abstract: | The sharp Jackson-type inequalities obtained by Taikov in the space L 2 and containing the best approximation and the modulus of continuity of first order are generalized to moduli of continuity of kth order (k = 2, 3, ... ). We also obtain exact values of the n-widths of the function classes F(k, r, Φ) and F k r (h), which are a generalization of the classes F(1, r, Φ) and F k r (h) studied by Taikov. |