@article{Vakarchuk_2016, title={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}, volume={68}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/1874}, abstractNote={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 $2\pi$ -periodic functions in the space $L_2$ with $(\psi , \beta)$-derivatives, introduced by Stepanets. These results take into account the classification of $(\psi , \beta)$-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.}, number={6}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Vakarchuk, S. B.}, year={2016}, month={Jun.}, pages={723-745} }