A weak ergodic theorem for infinite products of Lipschitzian mappings
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503206060 |
| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |