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A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces. (English) Zbl 1002.54025

In [J. Math. Anal. Appl. 202, No. 2, 433-449 (1996; Zbl 0855.54043)], E. Pap, O. Hadžić, and R. Mesiar introduced a type of contraction map known as \(C\)-contraction to prove some fixed point theorems in Menger spaces. In this paper the authors further extend the results of Pap-Hadžić-Mesiar to Menger spaces having more general types of \(t\)-norms. The authors also introduce another type of multivalued contraction to prove fixed point theorems on fuzzy metric spaces. This paper also contains some interesting examples.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
54E70 Probabilistic metric spaces

Citations:

Zbl 0855.54043
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References:

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