A Jackson-type theorem for averages of splines bounding a class of differentiable functions (Q801490)
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scientific article; zbMATH DE number 3879455
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Jackson-type theorem for averages of splines bounding a class of differentiable functions |
scientific article; zbMATH DE number 3879455 |
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A Jackson-type theorem for averages of splines bounding a class of differentiable functions (English)
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1985
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This paper improves the bounds for a variation of a Jackson-type theorem by \textit{A. Andreev}, \textit{V. A. Popov} and \textit{B. Sendov} [Mat. Zametki 26, 791-804 (1979; Zbl 0424.42004)] for best one-sided approximations by splines. The main theorem states how well a function can be approximated by the average of upper and lower bounding splines of a given order with respect to the \(L^ p[0,1]\) norm of a modified modulus of continuity.
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Jackson-type theorem
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best one-sided approximations
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modulus of continuity
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