Jackson-type inequalities with generalized modulus of continuity and exact values of the n-widths for the classes of (ψ,β)-differentiable functions in L_2. III - Vakarchuk, B. S. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
In the classes L^ψ_β ,2 of 2π -periodic (ψ , β)-differentiable functions for which f^ψ_β L_2, we determine the exact constants in Jackson-type inequalities for the characteristic of smoothness Λ_γ (f, t) = {1t ^t_0 \| Δ^γ_ h(f)\|^2dh }^1/2, t > 0, deternined by averaging the norm of the generalized difference relation Δ_ γh(f). For the classes of (ψ,β) -differentiable functions defined by using the characteristic of smoothness Λ_γ and the majorant Φ, satisfying numerous conditions, we find the exact values of some n-widths in L_2.