Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$

  • A. S. Serdyuk
  • O. I. Stepanets

Abstract

We continue the investigation of approximation properties of the space $S^p$. We introduce the notion of kth modulus of continuity and establish direct and inverse theorems on approximation in the space $S^p$ in terms of the best approximations and moduli of continuity. These theorems are analogous to the well-known theorems of Jackson and Bernshtein.
Published
25.01.2002
How to Cite
SerdyukA. S., and StepanetsO. I. “Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 54, no. 1, Jan. 2002, pp. 106-24, https://umj.imath.kiev.ua/index.php/umj/article/view/4044.
Section
Research articles