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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| Format: | Article |
| Language: | English |
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Wiley
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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| _version_ | 1832551789116784640 |
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| author | Simeon Reich Alexander J. Zaslavski |
| author_facet | Simeon Reich Alexander J. Zaslavski |
| author_sort | Simeon Reich |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-1feea90c676a4000b585fbdd6d675005 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1feea90c676a4000b585fbdd6d6750052025-02-03T06:00:31ZengWileyAbstract 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 |
| spellingShingle | Simeon Reich Alexander J. Zaslavski A weak ergodic theorem for infinite products of Lipschitzian mappings Abstract and Applied Analysis |
| title | 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_short | A weak ergodic theorem for infinite products of Lipschitzian
mappings |
| title_sort | weak ergodic theorem for infinite products of lipschitzian mappings |
| url | http://dx.doi.org/10.1155/S1085337503206060 |
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