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 (0,∞), obtain the exact Jackson-type inequalities for ω^w(f).