BEST POLYNOMIAL APPROXIMATIONS AND WIDTHS OF CERTAIN CLASSES OF FUNCTIONS IN THE SPACE L-2

In the paper exact values of the n-widths are found for the class of differentiable periodic functions in the space L-2[0, 27 pi], satisfying the condition ( integral(t)(0) T Omega(2/m)(m) ( f((r)) , T)dT )(m/2) <= Phi (t) where 0 < t <= pi/n, m, n, r is an element of N, Omega(m) (f((r)), T) is the generalized modulus of continuity of order in of the derivative f((r)) is an element of L-2[0, 2 pi], and Phi(t), 0 <= t < infinity is a continuous non-decreasing function, such that Phi(0) = 0 and Phi(t) > 0 for t > 0.