Geometric series of positive linear operators and the inverse Voronovskaya theorem on a compact interval
We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators and a class of Bernstein–Du...
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| Vydané v: | Journal of approximation theory Ročník 184; s. 163 - 175 |
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| Jazyk: | English |
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| Abstract | We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators and a class of Bernstein–Durrmeyer type operators. |
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| AbstractList | We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators and a class of Bernstein–Durrmeyer type operators. |
| Author | Ivan, Mircea Abel, Ulrich Păltănea, Radu |
| Author_xml | – sequence: 1 givenname: Ulrich surname: Abel fullname: Abel, Ulrich email: Ulrich.Abel@mnd.thm.de organization: Technische Hochschule Mittelhessen, University of Applied Sciences, Department MND, Wilhelm-Leuschner-Straße 13, 61169 Friedberg, Germany – sequence: 2 givenname: Mircea surname: Ivan fullname: Ivan, Mircea email: Mircea.Ivan@math.utcluj.ro organization: Technical University of Cluj-Napoca, Department of Mathematics, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania – sequence: 3 givenname: Radu surname: Păltănea fullname: Păltănea, Radu email: radupaltanea@yahoo.com, radu.paltanea@unitbv.ro organization: “Transilvania” University of Braşov, Faculty of Mathematics and Computer Science, Str. Iuliu Maniu nr. 50, 500091 Braşov, Romania |
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| Cites_doi | 10.1007/s00025-009-0363-3 10.1016/j.jmaa.2003.11.056 10.1006/jmaa.1997.5371 10.2140/pjm.1967.21.511 10.1007/s10587-010-0049-8 10.1007/s00009-010-0025-4 10.1016/j.jat.2008.11.002 10.1016/j.jat.2011.02.012 10.1006/jath.1996.3039 10.1007/s00009-011-0154-4 10.1080/00029890.2009.11920969 10.1016/0021-9045(76)90076-9 10.1007/s10474-006-0038-4 10.1016/j.jmaa.2010.07.026 10.1016/j.jmaa.2012.10.061 10.1016/0021-9045(80)90120-3 10.4153/CJM-1964-023-1 |
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| Keywords | Bernstein operators 41A35 41A36 Inverse Voronovskaya theorem Series of operators Positive linear operators 41A27 Bernstein–Durrmeyer type operators |
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| SubjectTerms | Bernstein operators Bernstein–Durrmeyer type operators Inverse Voronovskaya theorem Positive linear operators Series of operators |
| Title | Geometric series of positive linear operators and the inverse Voronovskaya theorem on a compact interval |
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