On the connection between the best approximation by algebraic polynomials and the modulus of smoothness of order r

Abstract

We introduce a family of asymmetric generalized translations. In terms of these operators, we define generalized moduli of smoothness for which the direct and inverse theorems of approximation theory are proved.

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Correspondence to M. K. Potapov.

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Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 25, Theory of Functions, 2007.

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Potapov, M.K., Berisha, F.M. On the connection between the best approximation by algebraic polynomials and the modulus of smoothness of order r . J Math Sci 155, 153–169 (2008). https://doi.org/10.1007/s10958-008-9217-x

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Keywords

  • Jacobi Polynomial
  • Algebraic Polynomial
  • Generalize Translation
  • Generalize Modulus
  • Inverse Theorem