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

Abstract

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.