Extension of contractive maps in the Menger probabilistic metric space. (English) Zbl 1152.54367
Summary: In this article, the topological properties of the Menger probabilistic metric spaces and the mappings between these spaces are studied. In addition, contractive and \(k\)-contractive mappings are introduced. As an application, a new fixed point theorem in a chainable Menger probabilistic metric space is proved.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 47H10 | Fixed-point theorems |
| 47S50 | Operator theory in probabilistic metric linear spaces |
| 54E70 | Probabilistic metric spaces |
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