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Contractions on probabilistic metric spaces: Examples and counterexamples. (English) Zbl 0689.60019

The authors compare two types of probabilistic contractions studied independently by V. M. Sehgal and A. T. Bharucha-Reid [Math. Systems Theory 6, 97-102 (1972; Zbl 0244.60004)] and T. L. Hicks [Zb. Rad. Prir.-Mat. Fak., Univ. Novom Sadu, Ser. Mat. 13, 63-72 (1983; Zbl 0574.54044)]. They give several interesting examples to show that the two contractions are independent and have their deficiencies. Further, they emphasize the need of a suitable notion of a probabilistic contraction which remains free from the deficiencies discussed by them.
Reviewer: S.L.Singh

MSC:

60B99 Probability theory on algebraic and topological structures
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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