Approximation of Urysohn operator with 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 a "rectangular isosceles triangle". As a special case, Bernstein-type polynomials are obtained. The Stancu asymptotic formulas for remainders are refined.
English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 3, pp 356-386.
Citation Example: Demkiv I. I., Makarov V. L. Approximation of Urysohn operator with operator polynomials of Stancu type // Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 318-343.