On some extremal problems in the theory of approximation of functions in the spaces $S^p,\quad 1 \leq p < \infty$

• Date: 2006
• Main Authors: Vakarchuk, S. B., Shchitov, A. N., Вакарчук, С. Б., Щитов, А. Н.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3455
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider and study properties of the smoothness characteristics $\Omega_m(f, t)_{S^p},\quad m \in \mathbb{N},\quad t > 0$, of functions $f(x)$ that belong to the space $S^p,\quad 1 \leq p < \infty$, introduced by Stepanets. Exact inequalities of the Jackson type are obtained, and th...