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The order of approximation to functions of the Zα. Class by means of positive linear operators

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Abstract

Let Cn (ϕ, α) be the upper bound for deviations of periodic functions which form the Zygmund class Zα,0 0<α<2 from a class of positive linear operators. A study is made of the conditions under which there exists a limit\(\mathop {\lim }\limits_{n \to \infty } \)nαCn(ϕ, α)=C(θ, α). An explicit expression is given for the functions C(ϕ,α).

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Translated from Matematicheskie Zametki, Vol. 4, No. 2, pp. 201–210, August, 1968.

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Bausov, L.I. The order of approximation to functions of the Zα. Class by means of positive linear operators. Mathematical Notes of the Academy of Sciences of the USSR 4, 612–617 (1968). https://doi.org/10.1007/BF01094961

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Keywords

  • Linear Operator
  • Explicit Expression
  • Periodic Function
  • Positive Linear Operator
  • Zygmund Class