Schweizer, B.; Sherwood, H.; Tardiff, R. M. Contractions on probabilistic metric spaces: Examples and counterexamples. (English) Zbl 0689.60019 Stochastica 12, No. 1, 5-17 (1988). 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 Cited in 2 ReviewsCited in 21 Documents MSC: 60B99 Probability theory on algebraic and topological structures 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems Keywords:fixed point; Menger space; simple space; probabilistic contractions Citations:Zbl 0244.60004; Zbl 0574.54044 PDFBibTeX XMLCite \textit{B. Schweizer} et al., Stochastica 12, No. 1, 5--17 (1988; Zbl 0689.60019) Full Text: EuDML