Strong converse inequality for linear combinations of Szász-Mirakjan operators
By means of the regularity of the differential operators generated by the Szász-Mirakjan operators, this paper further investigates the relation between the approximation rate of the linear combinations of the Szász-Mirakjan operators and the smoothness of the approximated function. We precisely giv...
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Published in | Journal of approximation theory Vol. 273; p. 105651 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.01.2022
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Subjects | |
Online Access | Get full text |
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Summary: | By means of the regularity of the differential operators generated by the Szász-Mirakjan operators, this paper further investigates the relation between the approximation rate of the linear combinations of the Szász-Mirakjan operators and the smoothness of the approximated function. We precisely give both the upper and lower bounds, which are of the same order, of the approximation of the linear combinations of these operators. Our results under some conditions include the direct theorem, the inverse theorem and the saturation of the uniform approximation of the linear combinations of these operators, and hence the approximation order of the uniform approximation of the linear combinations of the Szász-Mirakjan operators are further characterized. |
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ISSN: | 0021-9045 1096-0430 |
DOI: | 10.1016/j.jat.2021.105651 |