Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space Sp

@article{Stepanets2002DirectAI,
title={Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space Sp},
author={A. I. Stepanets and A. Serdyuk},
journal={Ukrainian Mathematical Journal},
year={2002},
volume={54},
pages={126-148}
}

We continue the investigation of approximation properties of the space Sp. We introduce the notion of kth modulus of continuity and establish direct and inverse theorems on approximation in the space Sp in terms of the best approximations and moduli of continuity. These theorems are analogous to the well-known theorems of Jackson and Bernshtein.