Approximation of Urysohn operator with operator polynomials of Stancu type - Demkiv, I. I.; Makarov, V. L. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
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.