Jackson Stechkin type inequalities with generalized moduli of continuity and widths of some classes of functions

In the Hilbert space L-2,L-mu[-1, 1] with Chebyshev weight mu(x) := 1/root 1- x(2), we obtain Jackson - Stechkin type inequalities between the value En-1(f)L-2,L-mu of the best approximation of a function f(x) by algebraic polynomials of degree at most n - 1 and the mth-order generalized modulus of continuity Omega(m) (D(r)f; t), where D is some second-order differential operator. For classes of functions W-p,m((2r)) (Psi) (m, r is an element of N, 1/(2r) < p <= 2) defined by the mentioned modulus of continuity and a given majorant Psi(t) (t >= 0), which satisfies certain constraints, we calculate the values of various n-widths in the space L-2,L-mu[-1, 1].