On the generalizations of Siegel's fixed point theorem (Q2735237)
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scientific article; zbMATH DE number 1640229
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the generalizations of Siegel's fixed point theorem |
scientific article; zbMATH DE number 1640229 |
Statements
20 October 2003
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complete generating space of quasi-metric family
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Downing-Kirk's fixed point theorem
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Caristi's theorem
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fuzzy metric spaces
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probabilistic metric spaces
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On the generalizations of Siegel's fixed point theorem (English)
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The authors prove a general version of Siegel's fixed point theorem in a complete generating space of quasi-metric family. As a consequence, they extend to the same spaces Downing-Kirk's fixed point theorem and Caristi's theorem. Moreover, they remark that, under very natural conditions, fuzzy metric spaces and probabilistic metric spaces are particular cases of generating spaces of quasimetric families. This allows to obtain applications of the main result to these spaces.
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