Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators
The present study introduces generalized λ-Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions. Then, a Voronovskaja-type theorem was given for the asympto...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5590439 |
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| _version_ | 1841524576513687552 |
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| author | Qing-Bo Cai Gülten Torun Ülkü Dinlemez Kantar |
| author_facet | Qing-Bo Cai Gülten Torun Ülkü Dinlemez Kantar |
| author_sort | Qing-Bo Cai |
| collection | DOAJ |
| description | The present study introduces generalized λ-Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions. Then, a Voronovskaja-type theorem was given for the asymptotic behavior for these operators. Finally, numerical examples and their graphs were given to demonstrate the convergence of Gm,λα,βf,x to fx with respect to m values. |
| format | Article |
| id | doaj-art-c9d75af3001b400d912827020fdc93ac |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c9d75af3001b400d912827020fdc93ac2025-02-03T05:52:58ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55904395590439Approximation Properties of Generalized λ-Bernstein–Stancu-Type OperatorsQing-Bo Cai0Gülten Torun1Ülkü Dinlemez Kantar2Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, ChinaKastamonu University, Faculty of Education, Mathematics and Science Education, Kastamonu, TurkeyGazi University, Faculty of Science, Department of Mathematics, Ankara, TurkeyThe present study introduces generalized λ-Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions. Then, a Voronovskaja-type theorem was given for the asymptotic behavior for these operators. Finally, numerical examples and their graphs were given to demonstrate the convergence of Gm,λα,βf,x to fx with respect to m values.http://dx.doi.org/10.1155/2021/5590439 |
| spellingShingle | Qing-Bo Cai Gülten Torun Ülkü Dinlemez Kantar Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators Journal of Mathematics |
| title | Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators |
| title_full | Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators |
| title_fullStr | Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators |
| title_full_unstemmed | Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators |
| title_short | Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators |
| title_sort | approximation properties of generalized λ bernstein stancu type operators |
| url | http://dx.doi.org/10.1155/2021/5590439 |
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