A weak ergodic theorem for infinite products of Lipschitzian mappings. (30th January 2003) - Reich, Simeon; Zaslavski, Alexander J.
Abstract : LetK be a bounded, closed, and convex subset of a Banach space. For a Lipschitzian self-mappingA ofK, we denote byLip ( A ) its Lipschitz constant. In this paper, we establish a convergence property of infinite products of Lipschitzian self-mappings ofK . We consider the set of all sequences{ A t   } t = 1 ∞ of such self-mappings with the propertylim sup t → ∞ Lip ( A t   ) ≤ 1 . Endowing it with an appropriate topology, we establish a weak ergodic theorem for the infinite products corresponding to generic sequences in this space.