EXACT CONSTANTS IN JACKSON-TYPE INEQUALITIES AND EXACT VALUES OF THE WIDTHS OF SOME CLASSES OF FUNCTIONS IN L_2

摘要

We find the exact values of the n-widths for the classes of periodic differentiable functions in L_2[0, 2π] satisfying the constraint m (f(r); t) dt ≤ Φ(h), where h > 0, m ∈ N, r ∈ Z+,Ω_m(f~((r)); t) is the generalized mth order continuity modulus of the derivative f~((r)0 ∈ L_2[0, 2π], while Φ(t) is an arbitrary increasing function such that Φ(0) = 0.