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....
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| Datum: | 2012 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2579 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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