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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 {At }t=1∞ 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.

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Handle: RePEc:wly:jnlaaa:v:2003:y:2003:i:2:p:67-74
DOI: 10.1155/S1085337503206060
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