A FIXED-POINT THEOREM IN PROBABILISTIC METRIC-SPACES AND AN APPLICATION

The notion of a (Psi, C)-contraction type multivalued mapping is intro duced. This notion is a generalization of the notion of C-contraction introduced by T. L. Hicks (Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fa k. Ser. Mat. 13, 1983, 63-72). A fixed point theorem for (Psi, C)-cont raction is proved. An application on the existence of a random fixed p oint for random operator f: M x Omega --> M, where (M, d) is a separab le metric space and (Omega, A, m) a measure space with a decomposable measure of (NSA)-type, is given. (C) 1996 Academic Press, Inc.