Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators
We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation theorems are obtained by using the classical modulus of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/1/5 |
| _version_ | 1797446192997597184 |
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| author | Yu-Jie Liu Wen-Tao Cheng Wen-Hui Zhang Pei-Xin Ye |
| author_facet | Yu-Jie Liu Wen-Tao Cheng Wen-Hui Zhang Pei-Xin Ye |
| author_sort | Yu-Jie Liu |
| collection | DOAJ |
| description | We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation theorems are obtained by using the classical modulus of continuity and <i>K</i>-functional. Finally, we derive the rate of convergence for functions with a derivative of bounded variation. The results show that the new operators have good approximation properties. |
| first_indexed | 2024-03-09T13:36:44Z |
| format | Article |
| id | doaj.art-1afb44a7c55846dd9771df96ce799d64 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:36:44Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-1afb44a7c55846dd9771df96ce799d642023-11-30T21:10:58ZengMDPI AGAxioms2075-16802022-12-01121510.3390/axioms12010005Approximation Properties of the Blending-Type Bernstein–Durrmeyer OperatorsYu-Jie Liu0Wen-Tao Cheng1Wen-Hui Zhang2Pei-Xin Ye3School of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaSchool of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaSchool of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, ChinaSchool of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, ChinaWe construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation theorems are obtained by using the classical modulus of continuity and <i>K</i>-functional. Finally, we derive the rate of convergence for functions with a derivative of bounded variation. The results show that the new operators have good approximation properties.https://www.mdpi.com/2075-1680/12/1/5modified Bernstein–Durrmeyer operatorsVoronovskaya-type theoremlocal approximationglobal approximation<i>K</i>-functionalmodulus of smoothness |
| spellingShingle | Yu-Jie Liu Wen-Tao Cheng Wen-Hui Zhang Pei-Xin Ye Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators Axioms modified Bernstein–Durrmeyer operators Voronovskaya-type theorem local approximation global approximation <i>K</i>-functional modulus of smoothness |
| title | Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators |
| title_full | Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators |
| title_fullStr | Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators |
| title_full_unstemmed | Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators |
| title_short | Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators |
| title_sort | approximation properties of the blending type bernstein durrmeyer operators |
| topic | modified Bernstein–Durrmeyer operators Voronovskaya-type theorem local approximation global approximation <i>K</i>-functional modulus of smoothness |
| url | https://www.mdpi.com/2075-1680/12/1/5 |
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