Random approximations and random fixed point theorems are stochastic generalization of classical approximations and fixed point theorems. The study of random fixed point theorems was initiated by Prague school of probabilities in 1950′s. The interest in these problems was enhanced after the publication of the survey article of Bharucha-Reid [5]. Random fixed point theory and applications have b...

Random fixed point theorems for condensing 1-set contraction selfmaps are known. But no random fixed point theorem for more general asymptotic 1-set contraction selfmaps is yet available. The purpose of this paper is to prove random fixed point theorems for such maps. 1. Introduction. Random fixed point theorems are stochastic versions of (classical or deterministic) fixed point theorems and ar...