On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer Operators
We construct a new family of univariate Chlodowsky type Bernstein-Stancu-Schurer operators and bivariate tensor product form. We obtain the estimates of moments and central moments of these operators, obtain weighted approximation theorem, establish local approximation theorems by the usual and the...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/6385451 |
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| _version_ | 1832549488071278592 |
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| author | Lian-Ta Shu Guorong Zhou Qing-Bo Cai |
| author_facet | Lian-Ta Shu Guorong Zhou Qing-Bo Cai |
| author_sort | Lian-Ta Shu |
| collection | DOAJ |
| description | We construct a new family of univariate Chlodowsky type Bernstein-Stancu-Schurer operators and bivariate tensor product form. We obtain the estimates of moments and central moments of these operators, obtain weighted approximation theorem, establish local approximation theorems by the usual and the second order modulus of continuity, estimate the rate of convergence, give a convergence theorem for the Lipschitz continuous functions, and also obtain a Voronovskaja-type asymptotic formula. For the bivariate case, we give the rate of convergence by using the weighted modulus of continuity. We also give some graphs and numerical examples to illustrate the convergent properties of these operators to certain functions and show that the new ones have a better approximation to functions f for one dimension. |
| format | Article |
| id | doaj-art-0aa6931b239c4600a58a4dabdbdbfd2a |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-0aa6931b239c4600a58a4dabdbdbfd2a2025-02-03T06:11:13ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/63854516385451On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer OperatorsLian-Ta Shu0Guorong Zhou1Qing-Bo Cai2School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, ChinaSchool of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaSchool of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, ChinaWe construct a new family of univariate Chlodowsky type Bernstein-Stancu-Schurer operators and bivariate tensor product form. We obtain the estimates of moments and central moments of these operators, obtain weighted approximation theorem, establish local approximation theorems by the usual and the second order modulus of continuity, estimate the rate of convergence, give a convergence theorem for the Lipschitz continuous functions, and also obtain a Voronovskaja-type asymptotic formula. For the bivariate case, we give the rate of convergence by using the weighted modulus of continuity. We also give some graphs and numerical examples to illustrate the convergent properties of these operators to certain functions and show that the new ones have a better approximation to functions f for one dimension.http://dx.doi.org/10.1155/2018/6385451 |
| spellingShingle | Lian-Ta Shu Guorong Zhou Qing-Bo Cai On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer Operators Journal of Function Spaces |
| title | On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer Operators |
| title_full | On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer Operators |
| title_fullStr | On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer Operators |
| title_full_unstemmed | On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer Operators |
| title_short | On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer Operators |
| title_sort | on the convergence of a family of chlodowsky type bernstein stancu schurer operators |
| url | http://dx.doi.org/10.1155/2018/6385451 |
| work_keys_str_mv | AT liantashu ontheconvergenceofafamilyofchlodowskytypebernsteinstancuschureroperators AT guorongzhou ontheconvergenceofafamilyofchlodowskytypebernsteinstancuschureroperators AT qingbocai ontheconvergenceofafamilyofchlodowskytypebernsteinstancuschureroperators |