On \(q\)-Baskakov-Mastroianni operators (Q444693)
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scientific article; zbMATH DE number 6066661
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(q\)-Baskakov-Mastroianni operators |
scientific article; zbMATH DE number 6066661 |
Statements
On \(q\)-Baskakov-Mastroianni operators (English)
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16 August 2012
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\(q\)-integers
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Stirling numbers
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linear positive operator
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Bohman-Korovkin theorem
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moduli of smoothness
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rate of convergence
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A general class of positive linear operators was defined by V. A. Baskakov and investigated by G. Mastroianni: see, e.g., Sections 5.2 and 5.3 in the monograph by \textit{F. Altomare} and \textit{M. Campiti} [Korovkin-type approximation theory and its applications. Berlin: Walter de Gruyter (1994; Zbl 0924.41001)].NEWLINENEWLINEIn this paper a \(q\)-analogue of this class is investigated. The authors define and study a new \(q\)-analogue of Stirling numbers and give explicit formulae for all moments of the new operators, based on \(q\)-integers.NEWLINENEWLINEThe rate of convergence is established in different function spaces. As particular cases, the \(q\)-analogues of some classical sequences are indicated.
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