Farthest points and subdifferential in \(p\)-normed spaces (Q938517)
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scientific article; zbMATH DE number 5313291
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Farthest points and subdifferential in \(p\)-normed spaces |
scientific article; zbMATH DE number 5313291 |
Statements
Farthest points and subdifferential in \(p\)-normed spaces (English)
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19 August 2008
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Summary: We study the farthest point mapping in a \(p\)-normed space \(X\) by virtue of the subdifferential of \(r(x)=\sup\{\| {x - z}\|^p:z\in M\}\), where \(M\) is a weakly sequentially compact subset of \(X\). We show that the set of all points in \(X\) which have a farthest point in \(M\) contains a dense \(G_{\delta }\) subset of \(X\).
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