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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| Veröffentlicht in: | Journal of approximation theory Jg. 273; S. 105651 |
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| Sprache: | Englisch |
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01.01.2022
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 105651 |
| Author | Xie, Linsen Wang, Shuli |
| Author_xml | – sequence: 1 givenname: Linsen surname: Xie fullname: Xie, Linsen email: linsenxie@lsu.edu.cn organization: Department of Mathematics, Lishui University, Lishui 323000, Zhejiang Province, China – sequence: 2 givenname: Shuli surname: Wang fullname: Wang, Shuli email: 605034939@qq.com organization: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang Province, China |
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| Keywords | Strong converse inequality 41A36 Linear combination Szász-Mirakjan operator 41A27 Regularity 41A17 |
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| References | Gupta, Tachev (b5) 2017 Wang (b8) 2019 Gonska, Zhou (b4) 1994; 53 Li (b6) 1997; 40 Wang, Xie (b9) 2019; 41 Totik (b7) 1994; 116 Xie, Wang, Zhao (b11) 2020 Ditzian, Totik (b3) 1987 Ditzian (b2) 2007; 3 Xie, Shi (b10) 2008; 23 Ding, Cao (b1) 2008; 155 Wang (10.1016/j.jat.2021.105651_b9) 2019; 41 Xie (10.1016/j.jat.2021.105651_b11) 2020 Gonska (10.1016/j.jat.2021.105651_b4) 1994; 53 Ding (10.1016/j.jat.2021.105651_b1) 2008; 155 Li (10.1016/j.jat.2021.105651_b6) 1997; 40 Ditzian (10.1016/j.jat.2021.105651_b3) 1987 Wang (10.1016/j.jat.2021.105651_b8) 2019 Xie (10.1016/j.jat.2021.105651_b10) 2008; 23 Ditzian (10.1016/j.jat.2021.105651_b2) 2007; 3 Gupta (10.1016/j.jat.2021.105651_b5) 2017 Totik (10.1016/j.jat.2021.105651_b7) 1994; 116 |
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| Title | Strong converse inequality for linear combinations of Szász-Mirakjan operators |
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