Fixed point theorems of the Banach and Krasnosel'skii type for mappings on \(m\)-tuple Cartesian product of Banach algebras and systems of generalized Gripenberg's equations (Q2847081)
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scientific article; zbMATH DE number 6204928
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fixed point theorems of the Banach and Krasnosel'skii type for mappings on \(m\)-tuple Cartesian product of Banach algebras and systems of generalized Gripenberg's equations |
scientific article; zbMATH DE number 6204928 |
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4 September 2013
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fixed point
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Banach algebra
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integral equation
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integro-differential system
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epidemic model
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blowing-up solution
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Fixed point theorems of the Banach and Krasnosel'skii type for mappings on \(m\)-tuple Cartesian product of Banach algebras and systems of generalized Gripenberg's equations (English)
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The authors prove some fixed point theorems of Banach and Krasnosel'skii types for mappings on the \(m\)-tuple Cartesian product of a Banach algebra \(X\) over \(\mathbb R\). Using these theorems, existence results for a system of integral equations of the Gripenberg's type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also given.
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