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A weak ergodic theorem for infinite products of Lipschitzian mappings

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  • Simeon Reich
  • Alexander J. Zaslavski

Abstract

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 { A t   } t = 1 ∞ of such self-mappings with the property lim 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.

Suggested Citation

  • Simeon Reich & Alexander J. Zaslavski, 2003. "A weak ergodic theorem for infinite products of Lipschitzian mappings," Abstract and Applied Analysis, Hindawi, vol. 2003, pages 1-8, January.
    • Handle: RePEc:hin:jnlaaa:256724
    DOI: 10.1155/S1085337503206060
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