@article{Serdyuk_Stepanets_2002, title={Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$}, volume={54}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/4044}, abstractNote={We continue the investigation of approximation properties of the space $S^p$. We introduce the notion of kth modulus of continuity and establish direct and inverse theorems on approximation in the space $S^p$ in terms of the best approximations and moduli of continuity. These theorems are analogous to the well-known theorems of Jackson and Bernshtein.}, number={1}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Serdyuk, A. S. and Stepanets, O. I.}, year={2002}, month={Jan.}, pages={106-124} }