Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type
Abstract In this paper, we introduce a family of GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type. We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaja...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-10-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1862-0 |
| _version_ | 1819092948919255040 |
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| author | Qing-Bo Cai Guorong Zhou |
| author_facet | Qing-Bo Cai Guorong Zhou |
| author_sort | Qing-Bo Cai |
| collection | DOAJ |
| description | Abstract In this paper, we introduce a family of GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type. We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaja type asymptotic formula for the bivariate λ-Bernstein–Kantorovich operators, as well as give some examples and their graphs to show the effect of convergence. |
| first_indexed | 2024-12-21T23:03:44Z |
| format | Article |
| id | doaj.art-73221020cb3748b282e5b06e1af616d4 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-21T23:03:44Z |
| publishDate | 2018-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-73221020cb3748b282e5b06e1af616d42022-12-21T18:47:13ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-10-012018111110.1186/s13660-018-1862-0Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich typeQing-Bo Cai0Guorong Zhou1School of Mathematics and Computer Science, Quanzhou Normal UniversitySchool of Applied Mathematics, Xiamen University of TechnologyAbstract In this paper, we introduce a family of GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type. We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaja type asymptotic formula for the bivariate λ-Bernstein–Kantorovich operators, as well as give some examples and their graphs to show the effect of convergence.http://link.springer.com/article/10.1186/s13660-018-1862-0B-continuous functionsB-differentiable functionsG B S $GBS$ operatorsBernstein–Kantorovich operatorsMixed modulus of smoothness |
| spellingShingle | Qing-Bo Cai Guorong Zhou Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type Journal of Inequalities and Applications B-continuous functions B-differentiable functions G B S $GBS$ operators Bernstein–Kantorovich operators Mixed modulus of smoothness |
| title | Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type |
| title_full | Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type |
| title_fullStr | Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type |
| title_full_unstemmed | Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type |
| title_short | Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type |
| title_sort | blending type approximation by gbs gbs operators of bivariate tensor product of λ bernstein kantorovich type |
| topic | B-continuous functions B-differentiable functions G B S $GBS$ operators Bernstein–Kantorovich operators Mixed modulus of smoothness |
| url | http://link.springer.com/article/10.1186/s13660-018-1862-0 |
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