Abstract and Applied Analysis
Volume 2003 (2003), Issue 2, Pages 67-74
A weak ergodic theorem for infinite products of Lipschitzian
Department of Mathematics, The Technion-Israel Institute of Technology, Haifa 32000, Israel
Received 16 May 2002
Copyright © 2003 Simeon Reich and Alexander J. Zaslavski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a bounded, closed, and convex subset of a Banach
space. For a Lipschitzian self-mapping of , we denote by its Lipschitz constant. In this paper, we establish a
convergence property of infinite products of Lipschitzian
self-mappings of . We consider the set of all sequences
of such self-mappings with the property
. Endowing it with an appropriate topology, we establish a weak ergodic
theorem for the infinite products corresponding to generic sequences in this space.