On contractive families and a fixed-point question of Stein
| dc.creator | Austin, Tim D. | |
| dc.date | 2006-08-21 | |
| dc.date.accessioned | 2026-07-07T07:22:00Z | |
| dc.date.available | 2026-07-07T07:22:00Z | |
| dc.description | In this paper we disprove the following conjectured generalization of the Contraction Mapping Theorem (due to J.D. Stein Jr.): Let X be a complete metric space and let F be a finite family of self-maps of X. Suppose there is a postive constant strictly less than 1 such that, for any two points x and y of X, some member of F contracts those points by a factor of at most that constant. Then some composition of members of F has a fixed point. We also show that the above does hold for a (continuous) commuting F containing only two maps. We conjecture that it holds for commuting F of any finite size. | |
| dc.description | 16 pages, 3 postscript figures, to appear in Mathematika | |
| dc.identifier | https://arxiv.org/abs/math/0608523 | |
| dc.identifier | http://arxiv.org/abs/math/0608523 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115504 | |
| dc.subject | Metric Geometry | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 54E40 | |
| dc.title | On contractive families and a fixed-point question of Stein | |
| dc.type | text |