Author : N.k. Agrawal,gupteshwar Gupta [ Volume No.:IV, Issue No.VI-Nov 2015] [Page No : 570-579] [2015]

We prove the existence of a common random fixed point of two asymptotically nonexpansive random operators through strong and weak convergences of an iterative process. The necessary and sufficient condition for the convergence of sequence of measurable functions to a random fixed point of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces is also established. Our random iteration scheme includes Ishikawa type and Mann type random iterations as special cases. The results obtained in this chapter represent an extension as well as refinement of previous known results. A new random iterative scheme for approximating random common fixed points of two random asymptotically nonexpansive random operators are defined and we have proved weak and strong convergence theorems in a uniformly convex Banach space.