RANDOM FIXED-POINT THEOREMS FOR VARIOUS CLASSES OF 1-SET-CONTRACTIVE MAPS IN BANACH-SPACES

Various random fixed point theorems for different classes of 1-set-con tractive random operator are proved. The class of I-set-contractive ra ndom operators includes condensing and nonexpansive random operators. It also includes semicontractive type random operators and locally alm ost nonexpansive random operators. Thus results due to S. Itoh [J. Mat h. Anal. Appl. 67 (1979), 261-273], T. C. Lin [Proc. Amer. Math. Sec. 103 (1988), 1129-1135; Proc. Amer. Math. Sec. 123 (1995), 1167-1176], and H. K. Xu [Proc. Amer. Math. Sec. 110 (1990), 495-500] are either e xtended or improved. (C) 1996 Academic Press, Inc.