Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4660860 | Topology and its Applications | 2006 | 10 Pages |
Abstract
It is proved that a commutative family of nonexpansive mappings of a complete R-tree X into itself always has a nonempty common fixed point set if X does not contain a geodesic ray. As a consequence of this, we show that any commuting family of edge preserving mappings of a connected reflexive graph G that contains no cycles or infinite paths always has at least one common fixed edge. This approach provides a new proof of the classical fixed edge theorem of Nowakowski and Rival. Several related results are also obtained.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology