Best mean-square approximation of functions defined on the real axis by entire functions of exponential type - Vakarchuk, S. B. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
Exact constants in Jackson-type inequalities are calculated in the space $L_2 (\mathbb{R})$ in the case where the quantity of the bestapproximation $\mathcal{A}_{σ}(f)$ is estimated from above by the averaged smoothness characteristic $Φ_2(f, t) = \cfrac 1t \int^t_0||Δ^2_h(f)||dh$.We also calculate the exact values of the average $ u$-widths of classes of functions defined by $Φ_2$.