Positive eigenvalues of countably contractive maps (Q596945)
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scientific article; zbMATH DE number 2082389
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive eigenvalues of countably contractive maps |
scientific article; zbMATH DE number 2082389 |
Statements
Positive eigenvalues of countably contractive maps (English)
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6 August 2004
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The Krasnoselskii theorem on positive eigenvectors (which is a variant of the Birkhoff-Kellog theorem in ordered Banach spaces) is generalized to countable \(k\)-set contractions in a normal cone. As an application, a result on the existence of positive eigenvalues for a positively homogeneous countably \(k\)-contractive monotone operator \(T\) satisfying \(T^pu\geq cu\) for some \(p\), \(u\) and \(c>0\) is obtained. The latter generalizes a result of \textit{I. Massabó} and \textit{C. A. Stuart} [Nonlinear Anal., Theory Methods Appl. 3, 35--44 (1979; Zbl 0422.47030)].
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nonlinear eigenvalue
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countably condensing maps
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countable \(k\)-set contractions
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Birkhoff-Kellog theoren
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Krasnoselskij theorem
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ordered Banach space
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0.7832744717597961
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0.7742199897766113
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0.7722659111022949
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