@article{Vakarchuk_2018, title={Generalized characteristics of smoothness and some extremе problems of the approximation theory of functions in the space $L_2 (R)$. I}, volume={70}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1627}, abstractNote={We consider the generalized characteristics of smoothness of the functions $\omega^w(f, t)$ and $\Lambda^w(f, t), t > 0,$ in the space $L_2(R)$ and, on the classes $L^{\alpha}_2 (R)$ defined with the help of fractional-order derivatives $\alpha \in (0,\infty)$, obtain the exact Jackson-type inequalities for $\omega^w(f)$.}, number={9}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Vakarchuk, S. B.}, year={2018}, month={Sep.}, pages={1166-1191} }