Random fixed points for several classes of 1-ball-contractive and 1-set-contractive random maps

A general random fixed point theorem for continuous random operators is pro ved. As applications, a number of random fixed points theorems for various classes of 1-set and 1-ball contractive random operators (e.g., operators o f contractive type with compact or completely continuous perturbations, ope rators of semicontractive type, etc.) are derived. Our results unify and ex tend most of the known random fixed points theorems. 1991 AMS Subject Class ification: 47H10 60H25. (C) 1999 Academic Press.