Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space Sp

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.

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Stepanets, A.I., Serdyuk, A.S. Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space Sp . Ukrainian Mathematical Journal 54, 126–148 (2002). https://doi.org/10.1023/A:1019701805228

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Keywords

  • Approximation Property
  • Inverse Theorem