An application of KKM-map principle (Q1205604)
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scientific article; zbMATH DE number 147572
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An application of KKM-map principle |
scientific article; zbMATH DE number 147572 |
Statements
An application of KKM-map principle (English)
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1 April 1993
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Let \(C\) be a convex subset of a Banach space \(X\), \(f: C\to X\) and \(g: C\to C\) be continuous (where, in addition, \(g\) is almost quasi-convex and onto), and \[ \bigl\{y\in C: \| g(x)- f(y)\|\geq \| g(y)- f(y)\|\;(x\in D)\bigr\} \] be compact for some \(D\subseteq C\). The author shows that then \(\| g(y_ 0)- f(y_ 0)\|= d(f(y_ 0),C)\) for some \(y_ 0\in C\).
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KKM-map principle
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convex subset of a Banach space
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almost quasi-convex and onto
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