Abstract. A random variational inequality is established which, in turn, is used to give a random best approximation theorem for a continuous set-valued mapping defined on a compact convex subset of a normed space. As an application, random fixed points are then derived. Finally, non-compact versions are also given. Our results include the corresponding results of Sehgal and Singh (1985) as special cases and our approach is different from those in the literature.

AMS Subject Classification (1991): 47H10, 49J41, 54C60, 46C05, 42A50

Keyword(s): Random variational inequality, random best approximation theorem, random fixed point theorem, nonself mapping

Received April 19, 1994, and in revised form February 21, 1995. (Registered under 5705/2009.)