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 proved. As applications, a number of random fixed points theorems for various classes of 1-set and 1-ball contractive random operators e.g., operators of contractive type with compact or completely continuous perturbations, operators of semicontractive type, etc.. are derived. Our results unify and extend most of the known random fixed points theorems. 1991 AMS Subject Classification: 47H10, 60H25.