Random fixed points of 1-set contractive random maps in Frechet spaces

A random fixed point theorem for more general 1-set-contractive random oper ators in Frechet spaces is proved. As applications, some random fixed point theorems for nonexpansive, semicontractive, and LANE random operators are also derived. Thus the results of Itoh [J. Math. Anal, Appl. 67 (1979), 261 -273], Lin [Proc. Amer. Math. Sec. 123 (1995), 1167-1176; Proc. Amer. Math. Soc. 103 (1988), 1129-1135], Shahzad [J. Math. Anal. Appl. 203 (1996), 712 -718], Tan and Yuan [Stochastic Anal. Appl. 15 (1997), 103-123], and Xu [Pr oc. Amer. Math. Soc. 110 (1990), 495-500], are extended. (C) 1999 Academic Press.