The approximate fixed point property in product spaces
| dc.creator | Kohlenbach, Ulrich | |
| dc.creator | Leustean, Laurentiu | |
| dc.date | 2005-10-26 | |
| dc.date.accessioned | 2026-07-07T06:47:56Z | |
| dc.date.available | 2026-07-07T06:47:56Z | |
| dc.description | In this paper we generalize to unbounded convex subsets C of hyperbolic spaces results obtained by W.A. Kirk and R. Espinola on approximate fixed points of nonexpansive mappings in product spaces $(C\times M)_\infty$, where M is a metric space and C is a nonempty, convex, closed and bounded subset of a normed or a CAT(0)-space. We extend the results further, to families $(C_u)_{u\in M}$ of unbounded convex subsets of a hyperbolic space. The key ingredient in obtaining these generalizations is a uniform quantitative version of a theorem due to Borwein, Reich and Shafrir, obtained by the authors in a previous paper using techniques from mathematical logic. Inspired by that, we introduce in the last section the notion of uniform approximate fixed point property for sets C and classes of self-mappings of C. The paper ends with an open problem. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510563 | |
| dc.identifier | http://arxiv.org/abs/math/0510563 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103820 | |
| dc.subject | Functional Analysis | |
| dc.subject | Logic | |
| dc.subject | 47H10, 47H09 (Primary) 03F10 (Secondary) | |
| dc.title | The approximate fixed point property in product spaces | |
| dc.type | text |