TY - JOUR AU - S. B. Vakarchuk AU - A. N. Shchitov PY - 2006/03/25 Y2 - 2024/03/28 TI - On some extremal problems in the theory of approximation of functions in the spaces $S^p,\quad 1 \leq p < \infty$ JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 58 IS - 3 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3455 AB - 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 the exact values of the widths of the classes of functions defined by using $\Omega_m(f, t)_{S^p},\quad m \in \mathbb{N},\quad t > 0$ are calculated. ER -