Constrained \(L_ p\)-approximation by generalized \(n\)-convex functions induced by ECT-systems (Q1890580)
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scientific article; zbMATH DE number 756637
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Constrained \(L_ p\)-approximation by generalized \(n\)-convex functions induced by ECT-systems |
scientific article; zbMATH DE number 756637 |
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Constrained \(L_ p\)-approximation by generalized \(n\)-convex functions induced by ECT-systems (English)
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5 July 1995
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The problem of finding a best \(L_ p\)-approximation \((1 \leq p < \infty)\) to a function in \(L_ p\) from a special subcone of generalized \(n\)- convex functions induced by an ECT-system is considered. Tchebychev splines with a countably infinite number of knots are introduced and best approximations are characterized in terms of local best approximations by these splines. Various properties of best approximations and their uniqueness in \(L_ 1\) are investigated. Some special results for generalized monotone and convex cases are obtained.
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\(L_ p\)-approximation
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generalized \(n\)-convex functions
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Tchebychev splines
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