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

  • S. B. Vakarchuk Днепропетр. ун-т им. А. Нобеля
  • A. N. Shchitov


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.
How to Cite
Vakarchuk, S. B., and A. N. Shchitov. “On Some Extremal Problems in the Theory of Approximation of Functions in the Spaces $S^p,\quad 1 \leq P &lt; \infty$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 3, Mar. 2006, pp. 303-16, https://umj.imath.kiev.ua/index.php/umj/article/view/3455.
Research articles