A weak ergodic theorem for infinite products of Lipschitzianmappings
Simeon Reich, Alexander J. Zaslavski · Abstract and Applied Analysis · 2003
Let K be a bounded, closed, and convex subset of a Banach space. For a Lipschitzian self‐mapping A of K, we denote by Lip(A) its Lipschitz constant. In this paper, we establish a convergence property of infinite products of Lipschitzian self‐mappings of K. We consider the set of all sequences of such self‐mappings with the property limsupt→∞Lip(At ) ≤ 1. Endowing it with an appropriate topology, we establish a weak ergodic theorem for the infinite products corresponding to generic sequences in this space.