Leray-Schauder alternatives in Banach algebra involving three operators with applications (Q2925788)
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scientific article; zbMATH DE number 6361919
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Leray-Schauder alternatives in Banach algebra involving three operators with applications |
scientific article; zbMATH DE number 6361919 |
Statements
27 October 2014
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Banach algebra
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sequentially weakly continuous
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fixed point theorems
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relatively weakly compact
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integral equations
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0.8970549
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0.87461954
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0.8477038
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0.84636474
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Leray-Schauder alternatives in Banach algebra involving three operators with applications (English)
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The object of the paper is the study of operator equations of the form NEWLINE\[NEWLINEx=AxBy+Cx,\tag{1}NEWLINE\]NEWLINE where the operators \(A\), \(B\) and \(C\) act on a Banach algebra \(E\) and \(A,C\) satisfy a generalized Lipschitz condition, while \(B\) is assumed to be weakly sequentially continuous (i.e., the image \(B\) of every weakly convergent sequence is weakly convergent). Under these and some others assumptions, a few fixed point theorems of Leray-Schauder type concerning (1) are established. An application to a functional nonlinear integral equation is also given.
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