Random Approximations and Fixed Point Theorems

As an application of our random variational inequality proved in this paper, the random versions of Fanʹs best approximation theorem for both single-valued and set-valued mappings are given. These results, in turn, are used to derive some random fixed point theorems for both nonself single-valued and set-valued mappings in normed spaces. Our random fixed point theorems are closely related to, but not comparable with results given by Engl, Lin, Reich, Seghal and Waters, Tan and Yuan, and Xu.