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 on the classes of functions L^α_2 (R) defined by the fractional derivatives of order α (0,∞ ) in the space L_2(R). The exact values 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).