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...
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Hindawi Limited
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503206060 |
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doaj-1feea90c676a4000b585fbdd6d6750052020-11-25T00:21:37ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092003-01-0120032677410.1155/S1085337503206060A weak ergodic theorem for infinite products of Lipschitzian mappingsSimeon Reich0Alexander J. Zaslavski1Department of Mathematics, The Technion-Israel Institute of Technology, Haifa 32000, IsraelDepartment of Mathematics, The Technion-Israel Institute of Technology, Haifa 32000, IsraelLet 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.http://dx.doi.org/10.1155/S1085337503206060 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Simeon Reich Alexander J. Zaslavski |
| spellingShingle |
Simeon Reich Alexander J. Zaslavski A weak ergodic theorem for infinite products of Lipschitzian mappings Abstract and Applied Analysis |
| author_facet |
Simeon Reich Alexander J. Zaslavski |
| author_sort |
Simeon Reich |
| title |
A weak ergodic theorem for infinite products of Lipschitzian
mappings |
| title_short |
A weak ergodic theorem for infinite products of Lipschitzian
mappings |
| title_full |
A weak ergodic theorem for infinite products of Lipschitzian
mappings |
| title_fullStr |
A weak ergodic theorem for infinite products of Lipschitzian
mappings |
| title_full_unstemmed |
A weak ergodic theorem for infinite products of Lipschitzian
mappings |
| title_sort |
weak ergodic theorem for infinite products of lipschitzian
mappings |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2003-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S1085337503206060 |
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