Jackson-type inequalities with generalized modulus of continuity and exact values of the $n$-widths of the classes of $(ψ,β)$-differential functions in $L_2$. I - Vakarchuk, S. B. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
For the generalized moduli of continuity, including the ordinary moduli of continuity and various their modifications, we establish the exact constants for Jackson-type inequalities in the classes of $2π$ -periodic functions in the space $L_2$ with $(ψ , β)$-derivatives, introduced by Stepanets. These results take into account the classification of $(ψ , β)$-derivatives and enable us to consider the major part of Jackson-type inequalities obtained earlier in the classes of differentiable functions$L_2^r,\; r \in N$, from the common point of view.