Abstract
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.
Citation
Simeon Reich. Alexander J. Zaslavski. "A weak ergodic theorem for infinite products of Lipschitzian mappings." Abstr. Appl. Anal. 2003 (2) 67 - 74, 30 January 2003. https://doi.org/10.1155/S1085337503206060
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