Random Fixed Point Theorems for Various Classes of 1-Set-Contractive Maps in Banach Spaces

Abstract

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 [J. Math. Anal. Appl.67(1979), 261–273], T. C. Lin [Proc. Amer. Math. Soc.103(1988), 1129–1135;Proc. Amer. Math. Soc.123(1995), 1167–1176], and H. K. Xu [Proc. Amer. Math. Soc.110(1990), 495–500] are either extended or improved.