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Generalized contraction mapping principles in probabilistic metric spaces. (English) Zbl 1050.47052

Let \((S,{\mathcal F}, T)\) be a complete Menger space and \(f:S\to S\) an operator. The authors give conditions which imply that \(f\) has a unique fixed point which is globally attractive. The case when \((S, {\mathcal F} , T)\) is a complete random normed space is also discussed. Some applications are given.

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
47S50 Operator theory in probabilistic metric linear spaces
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