Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings
The generic convergence of infinite products of nonexpansive mappings was established in a 1999 paper of ours. In the present paper, such results are extended to infinite products of uniformly locally nonexpansive mappings. In particular, the convergence of infinite products of uniformly locally con...
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2025-02-01
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| author | Simeon Reich Alexander J. Zaslavski |
| author_facet | Simeon Reich Alexander J. Zaslavski |
| author_sort | Simeon Reich |
| collection | DOAJ |
| description | The generic convergence of infinite products of nonexpansive mappings was established in a 1999 paper of ours. In the present paper, such results are extended to infinite products of uniformly locally nonexpansive mappings. In particular, the convergence of infinite products of uniformly locally contractive mappings, as well as its stability, are proved. Moreover, the Baire category approach and the porosity notion are used to show that most sequences of uniformly locally nonexpansive mappings are, in fact, uniformly locally contractive. |
| format | Article |
| id | doaj-art-2fa74fa768ae4f2ca647eba57eadbb16 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-2fa74fa768ae4f2ca647eba57eadbb162025-08-20T02:59:15ZengMDPI AGMathematics2227-73902025-02-0113572310.3390/math13050723Convergence of Infinite Products of Uniformly Locally Nonexpansive 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, IsraelThe generic convergence of infinite products of nonexpansive mappings was established in a 1999 paper of ours. In the present paper, such results are extended to infinite products of uniformly locally nonexpansive mappings. In particular, the convergence of infinite products of uniformly locally contractive mappings, as well as its stability, are proved. Moreover, the Baire category approach and the porosity notion are used to show that most sequences of uniformly locally nonexpansive mappings are, in fact, uniformly locally contractive.https://www.mdpi.com/2227-7390/13/5/723complete metric spacefixed pointinexact iterateinfinite productnonexpansive mapping |
| spellingShingle | Simeon Reich Alexander J. Zaslavski Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings Mathematics complete metric space fixed point inexact iterate infinite product nonexpansive mapping |
| title | Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings |
| title_full | Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings |
| title_fullStr | Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings |
| title_full_unstemmed | Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings |
| title_short | Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings |
| title_sort | convergence of infinite products of uniformly locally nonexpansive mappings |
| topic | complete metric space fixed point inexact iterate infinite product nonexpansive mapping |
| url | https://www.mdpi.com/2227-7390/13/5/723 |
| work_keys_str_mv | AT simeonreich convergenceofinfiniteproductsofuniformlylocallynonexpansivemappings AT alexanderjzaslavski convergenceofinfiniteproductsofuniformlylocallynonexpansivemappings |