Abstract
The first fixed point theorem in probabilistic metric spaces was proved by Sehgal and Barucha-Reid [272] for mappings f : S → S, where (S, F, T M) is a Menger space. Further development of the fixed point theory in a more general Menger space (S, F, T) was connected with investigations of the structure of the t-norm T. Very soon the problem was in some sense completely solved. Namely, if we restrict ourselves to complete Menger spaces (S, F, T), where T is a continuous t-norm, then any probabilistic q-contraction f : S → S has a fixed point if and only if the t-norm is of H-type.
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© 2001 Springer Science+Business Media Dordrecht
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Hadžić, O., Pap, E. (2001). Probabilistic B-contraction principles for single-valued mappings. In: Fixed Point Theory in Probabilistic Metric Spaces. Mathematics and Its Applications, vol 536. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1560-7_3
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DOI: https://doi.org/10.1007/978-94-017-1560-7_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5875-1
Online ISBN: 978-94-017-1560-7
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