A Survey of Results on the Limit -Bernstein Operator
The limit -Bernstein operator emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution, which is used in the -boson theory to describe the energy distribution in a -analogue of the coherent state. At the same time, this operator bears a significant role i...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/159720 |
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| _version_ | 1832555963204239360 |
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| author | Sofiya Ostrovska |
| author_facet | Sofiya Ostrovska |
| author_sort | Sofiya Ostrovska |
| collection | DOAJ |
| description | The limit -Bernstein operator emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution, which is used in the -boson theory to describe the energy distribution in a -analogue of the coherent state. At the same time, this operator bears a significant role in the approximation theory as an exemplary model for the study of the convergence of the -operators. Over the past years, the limit -Bernstein operator has been studied widely from different perspectives. It has been shown that is a positive shape-preserving linear operator on with . Its approximation properties, probabilistic interpretation, the behavior of iterates, and the impact on the smoothness of a function have already been examined. In this paper, we present a review of the results on the limit -Bernstein operator related to the approximation theory. A complete bibliography is supplied. |
| format | Article |
| id | doaj-art-e288714b1106445d8019ab0d90160063 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e288714b1106445d8019ab0d901600632025-02-03T05:46:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/159720159720A Survey of Results on the Limit -Bernstein OperatorSofiya Ostrovska0Department of Mathematics, Atilim University, Ankara 06836, TurkeyThe limit -Bernstein operator emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution, which is used in the -boson theory to describe the energy distribution in a -analogue of the coherent state. At the same time, this operator bears a significant role in the approximation theory as an exemplary model for the study of the convergence of the -operators. Over the past years, the limit -Bernstein operator has been studied widely from different perspectives. It has been shown that is a positive shape-preserving linear operator on with . Its approximation properties, probabilistic interpretation, the behavior of iterates, and the impact on the smoothness of a function have already been examined. In this paper, we present a review of the results on the limit -Bernstein operator related to the approximation theory. A complete bibliography is supplied.http://dx.doi.org/10.1155/2013/159720 |
| spellingShingle | Sofiya Ostrovska A Survey of Results on the Limit -Bernstein Operator Journal of Applied Mathematics |
| title | A Survey of Results on the Limit -Bernstein Operator |
| title_full | A Survey of Results on the Limit -Bernstein Operator |
| title_fullStr | A Survey of Results on the Limit -Bernstein Operator |
| title_full_unstemmed | A Survey of Results on the Limit -Bernstein Operator |
| title_short | A Survey of Results on the Limit -Bernstein Operator |
| title_sort | survey of results on the limit bernstein operator |
| url | http://dx.doi.org/10.1155/2013/159720 |
| work_keys_str_mv | AT sofiyaostrovska asurveyofresultsonthelimitbernsteinoperator AT sofiyaostrovska surveyofresultsonthelimitbernsteinoperator |