Fixed points on star-shaped subsets of convex metric spaces (Q1090964)
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scientific article; zbMATH DE number 4009314
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fixed points on star-shaped subsets of convex metric spaces |
scientific article; zbMATH DE number 4009314 |
Statements
Fixed points on star-shaped subsets of convex metric spaces (English)
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1987
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Let T be a Kannan mapping of a bounded closed star-shaped subset K of a convex metric space X, into itself and for every closed star-shaped subset F of K, \(\sup_{y\in F}d(y,Ty)<(diameter\) of F). It is proved that if there exists a minimal T-invariant star-shaped subset \(K^*\) of K then T has a unique fixed point in K.
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Kannan mapping
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convex metric space
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star-shaped subset
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