Generalized characteristics of smoothness and some extremе problems of the approximation theory of functions in the space $L_2 (R)$. I - Vakarchuk, S. B. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
We consider the generalized characteristics of smoothness of the functions $ω^w(f, t)$ and $Λ^w(f, t), t > 0,$ in the space$L_2(R)$ and, on the classes $L^{α}_2 (R)$ defined with the help of fractional-order derivatives $α \in (0,∞)$, obtain the exactJackson-type inequalities for $ω^w(f)$.