Nonlinear superposition operators on space \(C([0,1],\mathbb{E})\) (Q1323171)
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scientific article; zbMATH DE number 566980
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear superposition operators on space \(C([0,1],\mathbb{E})\) |
scientific article; zbMATH DE number 566980 |
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Nonlinear superposition operators on space \(C([0,1],\mathbb{E})\) (English)
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10 May 1994
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Given a Banach space \(E\), the author shows that the Lipschitz condition \[ \| Fx_ 1- Fx_ 2\|\leq k(r) \| x_ 1-x_ 2\| \qquad (\| x_ 1\|, \| x_ 2\|\leq r) \] and the Darbo condition \[ \chi (F\Omega)\leq k(r)\chi(\Omega) \] for the Nemytskij operator \[ F: C([0,1],E)\to C([0,1], E) \] are equivalent. This generalizes the corresponding result for \(E=\mathbb{R}\) by the reviewer [J. Anal. Appl. 83, No. 1, 251-263 (1981; Zbl 0495.45007)].
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Lipschitz condition
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Darbo condition
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Nemytskij operator
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0.9257405
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0.9221478
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0.91913104
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0.9146904
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0.9115396
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0.90690404
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