Approximation properties of λ-Kantorovich operators
Abstract In the present paper, we study a new type of Bernstein operators depending on the parameter λ∈[−1,1] $\lambda\in[-1,1]$. The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian–Totik modulu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1795-7 |
| Summary: | Abstract In the present paper, we study a new type of Bernstein operators depending on the parameter λ∈[−1,1] $\lambda\in[-1,1]$. The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian–Totik modulus of smoothness is proved. Also, a Grüss–Voronovskaja type theorem for λ-Kantorovich operators is provided. Some numerical examples which show the relevance of the results are given. |
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| ISSN: | 1029-242X |