Contraction maps on probabilistic metric spaces (Q1191651)
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scientific article; zbMATH DE number 60462
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Contraction maps on probabilistic metric spaces |
scientific article; zbMATH DE number 60462 |
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Contraction maps on probabilistic metric spaces (English)
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27 September 1992
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The well-known Banach contraction principle states that every contraction mapping on a complete metric space has a unique fixed point. However, an exact analogue of this result is not true in general in probabilistic metric space (PM-space). In this paper, by imposing a growth condition on the distance distribution function, it is proved that for a large class of triangle functions, contraction mappings on complete PM-spaces have a unique fixed point.
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Banach contraction principle
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unique fixed point
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distance distribution function
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triangle function
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contraction mappings
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complete PM-spaces
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