Essential \({\mathcal U}_c^\kappa\)-type maps and Birkhoff--Kellogg theorems (Q1773284)
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scientific article; zbMATH DE number 2161824
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Essential \({\mathcal U}_c^\kappa\)-type maps and Birkhoff--Kellogg theorems |
scientific article; zbMATH DE number 2161824 |
Statements
Essential \({\mathcal U}_c^\kappa\)-type maps and Birkhoff--Kellogg theorems (English)
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26 April 2005
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A new interesting continuation theorem for \({\mathcal U}_c^\kappa\)-type maps is proved. The analysis involved is elementary and combines properties of the Minkowski functional with fixed point theory for self maps. Using their new homotopy theorem, they prove an ``invariant direction'' result for particular classes of maps. The theory and results presented in this paper extend and unify previously known results.
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continuation theorem
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Minkowski functional
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homotopy theorem
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Birkhoff--Kellogg theorem
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essential \({\mathcal U}_c^\kappa\)-type map
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