Demkiv I. I.
Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 318-343
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.
Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1172-1181
We generalize properties of the Bernstein polynomials to the Bernstein-type operator polynomials approximating the Urison operator.