Best Polynomial Approximations in L_2 and Widths of Some Classes of Functions - Vakarchuk, S. B.; Shchitov, A. N. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We obtain the exact values of extremal characteristics of a special form that connect the best polynomial approximations of functions f(x) ∈ L_2^r(r ∈ ℤ_+) and expressions containing moduli of continuity of the kth order ω_k(f^(r), t). Using these exact values, we generalize the Taikov result for inequalities that connect the best polynomial approximations and moduli of continuity of functions from L_2. For the classes F (k, r, Ψ*) defined by ω_k(f^(r), t) and the majorant Ψ(t)=t^4k/π^2, we determine the exact values of different widths in the space L_2.