A generalization of the Lupaș \(q\)-analogue of the Bernstein operator
We introduce a Stancu type generalization of the Lupaș \(q\)-analogue of the Bernstein operator via the parameter \(\alpha\). The construction of our operator is based on the generalization of Gauss identity involving \(q\)-integers. We establish the convergence of our sequence of operators in the...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2016-12-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/1090 |
| Summary: | We introduce a Stancu type generalization of the Lupaș \(q\)-analogue of the Bernstein operator via the parameter \(\alpha\). The construction of our operator is based on the generalization of Gauss identity involving \(q\)-integers. We establish the convergence of our sequence of operators in the strong operator topology to the identity, estimating the rate of convergence by using the second order modulus of smoothness. For \(\alpha\) and \(q\) fixed, we study the limit operator of our sequence of operators taking into account the relationship between two consecutive terms of the constructed sequence of operators.
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| ISSN: | 2457-6794 2501-059X |