A proof of the mean ergodic theorem for nonexpansive mappings in Banach space
Norimichi Hirano · Proceedings of the American Mathematical Society · 1980
Let C be a closed convex subset of a uniformly convex Banach space. Let T : C → C T:C \to C be a nonexpansive mapping. In this paper, we deal with the weak convergence of the arithmetical means of the sequence T n x {T^n}x , and give a new proof of the mean ergodic theorem for nonexpansive mappings.