Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators
Abstract This paper is concerned with the ( p , q ) $(p,q)$ -analog of Bernstein operators. It is proved that, when the function is convex, the ( p , q ) $(p,q)$ -Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that veri...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1111-3 |
| _version_ | 1811301624260329472 |
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| author | Shin Min Kang Arif Rafiq Ana-Maria Acu Faisal Ali Young Chel Kwun |
| author_facet | Shin Min Kang Arif Rafiq Ana-Maria Acu Faisal Ali Young Chel Kwun |
| author_sort | Shin Min Kang |
| collection | DOAJ |
| description | Abstract This paper is concerned with the ( p , q ) $(p,q)$ -analog of Bernstein operators. It is proved that, when the function is convex, the ( p , q ) $(p,q)$ -Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved. |
| first_indexed | 2024-04-13T07:12:12Z |
| format | Article |
| id | doaj.art-373681921c8e462d8891cac006a27160 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-13T07:12:12Z |
| publishDate | 2016-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-373681921c8e462d8891cac006a271602022-12-22T02:56:50ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-06-012016111010.1186/s13660-016-1111-3Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operatorsShin Min Kang0Arif Rafiq1Ana-Maria Acu2Faisal Ali3Young Chel Kwun4Department of Mathematics and RINS, Gyeongsang National UniversityDepartment of Mathematics and Statistics, Virtual University of PakistanDepartment of Mathematics and Informatics, Lucian Blaga University of SibiuCenter for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya UniversityDepartment of Mathematics, Dong-A UniversityAbstract This paper is concerned with the ( p , q ) $(p,q)$ -analog of Bernstein operators. It is proved that, when the function is convex, the ( p , q ) $(p,q)$ -Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved.http://link.springer.com/article/10.1186/s13660-016-1111-3( p , q ) $(p,q)$ -Bernstein operators( p , q ) $(p,q)$ -calculusVoronovskaja type theoremK-functionalDitzian-Totik first order modulus of smoothness |
| spellingShingle | Shin Min Kang Arif Rafiq Ana-Maria Acu Faisal Ali Young Chel Kwun Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators Journal of Inequalities and Applications ( p , q ) $(p,q)$ -Bernstein operators ( p , q ) $(p,q)$ -calculus Voronovskaja type theorem K-functional Ditzian-Totik first order modulus of smoothness |
| title | Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators |
| title_full | Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators |
| title_fullStr | Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators |
| title_full_unstemmed | Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators |
| title_short | Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators |
| title_sort | some approximation properties of p q p q bernstein operators |
| topic | ( p , q ) $(p,q)$ -Bernstein operators ( p , q ) $(p,q)$ -calculus Voronovskaja type theorem K-functional Ditzian-Totik first order modulus of smoothness |
| url | http://link.springer.com/article/10.1186/s13660-016-1111-3 |
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