A fixed point theorem in probabilistic metric spaces and an application

Abstract

The notion of a (ψ, C)-contraction type multivalued mapping is introduced. This notion is a generalization of the notion of C-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 operator f : M × Ω → M, where (M, d) is a separable metric space and (Ω, script A sign, ℳ) a measure space with a decomposable measure of (NSA)-type, is given. © 1996 Academic Press, Inc.