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: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-06-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1111-3 |
| Summary: | 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. |
|---|---|
| ISSN: | 1029-242X |