Best Polynomial Approximations and Widths of Certain Classes of Functions in the Space \( L_2 \) - Yusupov, Gulzorkhon Amirshoevich (Eurasian Mathematical Journal, 2013)
In the paper exact values of the n-widths are found for the class of differentiable periodic functions in the space L2[0, 2π], satisfying the condition (_0^t τ Ω_2/m^m(f(r),τ)dτ)^m/2 ≤ Φ(t), where 0 < t ≤ π/n, m, n, r N, Ω_m(f(r),τ) is the generalized modulus of continuity of order m of the derivative f(r) L^2[0,2π], and Φ(t) is a continuous non-decreasing function, such that Φ(0) = 0 and Φ(t) > 0 for t > 0.