Approximation of functions of bounded variation by integrated Meyer-König and Zeller operators of finite type (Q2915442)
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scientific article; zbMATH DE number 6083273
| Language | Label | Description | Also known as |
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| English | Approximation of functions of bounded variation by integrated Meyer-König and Zeller operators of finite type |
scientific article; zbMATH DE number 6083273 |
Statements
Approximation of functions of bounded variation by integrated Meyer-König and Zeller operators of finite type (English)
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17 September 2012
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Meyer-König and Zeller operators
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rate of convergence
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function of bounded variation
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\textit{W. Meyer-König} and \textit{K. Zeller} [Stud. Math. 19, 89--94 (1960; Zbl 0091.14506)] defined a sequence of linear positive operators associated with each continuous real-valued function defined on the unit interval. \textit{I. Gavrea} and the author [in: Proceedings of the fifth international conference on functional analysis and approximation theory, Acquafredda di Maratea, Italy, 2004. Palermo: Circolo Matemàtico di Palermo. 375--394 (2005; Zbl 1136.41310)] introduced and studied a sequence of Meyer-König and Zeller operators of finite type and also its Durrmeyer counterpart. Here the author studies the approximation properties of the foregoing Durrmeyer counterpart operators when the associated real-valued function is of bounded variation and not necessarily continuous on the unit interval.
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