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Approximation of the Urysohn operator by operator polynomials of Stancu type

We study a one-parameter family of positive polynomial operators of one and two variables that approximate the Urysohn operator. In the case of two variables, the integration domain is an “isosceles right triangle.” As a special case, Bernstein-type polynomials are obtained. The Stancu asymptotic formulas for remainders are refined.

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Author information

Correspondence to V. L. Makarov.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 3, pp. 318–343, March, 2012.

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Makarov, V.L., Demkiv, I.I. Approximation of the Urysohn operator by operator polynomials of Stancu type. Ukr Math J 64, 356–386 (2012). https://doi.org/10.1007/s11253-012-0652-y

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Keywords

  • Asymptotic Estimate
  • Bernstein Polynomial
  • Obvious Generalization
  • Bernstein Operator
  • Operator Polynomial