Selections and approximations of convex-valued equivariant mappings (Q388655)
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scientific article; zbMATH DE number 6242611
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Selections and approximations of convex-valued equivariant mappings |
scientific article; zbMATH DE number 6242611 |
Statements
Selections and approximations of convex-valued equivariant mappings (English)
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3 January 2014
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convex-valued multifunction
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Carathéodory selection
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graph-approximation
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\(G\)-space
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equivariant selection
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set-valued mapping
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Selection, almost-selection and graph-approximation theorems for \(G\)-equivariant multifunctions acting between \(G\)-spaces are presented. All considered multifunctions have closed, convex values in a separable Banach representation of a group \(G\). \(G\)-equivariant Carathéodory selections for separately measurable and separately lsc multifunctions defined on the adequate product spaces are carefully studied. The results are applicable in fixed point thery for set-valued maps.NEWLINENEWLINE Remark: It would be interesting to have similar theorems in the case of multifunctions with decomposable (instead of convex) values.
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