2019
Том 71
№ 8

All Issues

Demkiv I. I.

Articles: 2
Article (English)

Approximation of Urysohn operator with operator polynomials of Stancu type

Demkiv I. I., Makarov V. L.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

On properties of Bernstein-typ operator p0lynomials approximating the Urison operator.

Demkiv I. I.

↓ Abstract   |   Full text (.pdf)

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.