On the theory of probabilistic metric spaces with applications. (English) Zbl 0614.60010
The purpose of this paper is to investigate the theory of probabilistic metric spaces and its applications. In § 1 we introduce a kind of Menger probabilistic metric space. By virtue of their basic properties and the Menger-Hausdorff metric defined for this kind of spaces we obtain in § 2 some fixed point theorems for multi-valued mappings on probabilistic metric spaces.
In addition, in § 3 we present some fixed point theorems for one- valued mappings on probabilistic metric spaces, which generalize and improve some recent results of I. Istrăteşcu [Rev. Roum. Math. Pures Appl. 26, 431-435 (1981; Zbl 0476.60006)]; V. M. Sehgal and A. T. Bharucha-Reid [Math. Syst. Theory 6, 97-102 (1972; Zbl 0244.60004)] and G. Bocşan [Proc. 5th Conf. Probab. Theory, Braşov 1974, 153-155 (1977; Zbl 0439.60068)].
In addition, in § 3 we present some fixed point theorems for one- valued mappings on probabilistic metric spaces, which generalize and improve some recent results of I. Istrăteşcu [Rev. Roum. Math. Pures Appl. 26, 431-435 (1981; Zbl 0476.60006)]; V. M. Sehgal and A. T. Bharucha-Reid [Math. Syst. Theory 6, 97-102 (1972; Zbl 0244.60004)] and G. Bocşan [Proc. 5th Conf. Probab. Theory, Braşov 1974, 153-155 (1977; Zbl 0439.60068)].
MSC:
| 60B99 | Probability theory on algebraic and topological structures |
| 60H25 | Random operators and equations (aspects of stochastic analysis) |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
Keywords:
probabilistic metric spaces; Menger-Hausdorff metric; fixed point theorems for multi-valued mappingsReferences:
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