Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space $L_2 (R)$. II - Vakarchuk, S. B. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
In the second part of the paper, we establish the exact Jackson-type inequalities for the characteristic of smoothness $Λ^w$ onthe classes of functions $L^{α}_2 (R)$ defined by the fractional derivatives of order $α \in (0,∞ )$ in the space $L_2(R)$. The exactvalues of the mean $ u$ -widths for the classes of functions, defined by the generalized characteristics of smoothness $ω w$ and$Λ w$ are also computed in $L_2(R)$.