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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Bibliographic Details
Published in:Journal of approximation theory Vol. 273; p. 105651
Main Authors: Xie, Linsen, Wang, Shuli
Format: Journal Article
Language:English
Published: Elsevier Inc 01.01.2022
Subjects:
Linear combination
Regularity
Strong converse inequality
Szász-Mirakjan operator
Strong converse inequality
41A36
Linear combination
Szász-Mirakjan operator
41A27
Regularity
41A17
ISSN:0021-9045, 1096-0430
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.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2021.105651