Properties of minimal invariant sets for nonexpansive mappings (Q1305305)
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scientific article; zbMATH DE number 1346181
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Properties of minimal invariant sets for nonexpansive mappings |
scientific article; zbMATH DE number 1346181 |
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Properties of minimal invariant sets for nonexpansive mappings (English)
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25 June 2000
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Let \(C\) be a nonempty, weakly compact, convex subset of a Banach space \(X\). Let the mapping \(T:C\to C\) be nonexpansive, i.e. such that \(\|Tx- Ty\|\leq\|x-y\|\), \(\forall x,y\in C\). A minimal invariant set is a minimal element of the family of all \(T\)-invariant sets with respect to the order generated by inclusion. The author proves some properties of minimal invariant sets and states some open problems.
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nonexpansive mappings
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minimal invariant sets
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