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-contractive random operator are proved. The class of 1-set-contractive random operators includes condensing and nonexpansive random operators. It also includes semicontractive type random operators and locally almost nonexpansive random operators. Thus results due to S. Itoh w J. Math. Anal. Appl. 67 1979., 261]273x, T. C. Lin w Proc. Amer. Math. Soc. 103 1988., 1129]1135; Proc. Amer. Math. Soc. 123 1995., 1167]1176x, and H. K. XuwProc. Amer. Math. Soc. 110 1990., 495]500x are either extended or improved.