Random Fixed-Point Theorems and Approximation in Cones

A very general random fixed point theorem is first proved. As applications, some random approximation theorems and random fixed-point theorems are obtained. Recent results due to Itoh [J. Math. Anal. Appl.67 (1979), 261-273], Lin [Proc. Amer. Math. Soc.103 (1988), 502-506], and Xu [Proc. Amer. Math. Soc.110 (1990), 495-500] either are improved or are direct consequences of our results. The stochastic versions of the recent results of Lin [1988] and Li [Proc. Amer. Math. Soc.97 (1986), 277-280] are also given.