A Fixed Point Theorem in Probabilistic Metric Spaces and an Application

AbstractThe notion of a (Ψ,C)-contraction type multivalued mapping is introduced. This notion is a generalization of the notion ofC-contraction introduced by T. L. Hicks (Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat.13, 1983, 63–72). A fixed point theorem for (Ψ,C)-contraction is proved. An application on the existence of a random fixed point for random operatorf:M×Ω→M, where (M,d) is a separable metric space and (Ω,A,m) a measure space with a decomposable measure of (NSA)-type, is given