MEAN ERGODIC THEOREMS FOR A SEQUENCE OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Masanori Akatsuka, Koji Aoyama, Wataru Takahashi · Tokyo Tech Research Repository (Tokyo Institute of Technology) · 2008
Let C be a closed convex subset of a Hilbert space and {Tn} a sequence of nonexpansive self-mappings of C. Then we consider the following iterative sequence {zn}: x1 = x ∈ C, xn+1 = Tnxn, and zn =1 /n n=1 xk for n ∈ . In this paper, we obtain a weak convergence theorem for such a sequence {zn}. Using our result, we get a nonlinear ergodic theorem which is a generalization of Baillon (2). Further we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings.