Approximation of the Urysohn operator by operator polynomials of Stancu type - Demkiv, I.I.; Makarov, V.L. (Український математичний журнал, 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 an “isosceles right triangle.” As a special case, Bernstein-type polynomials are obtained. The Stancu asymptotic formulas for remainders are refined.