Let be a -hyperconvex -quasimetric space, and stand for the set of all (nonempty) externally -hyperconvex subsets of .
The following are the main results in the paper:
Theorem 1. Let be a nonempty set, and be a mapping. There exists then a mapping which selects [i.e.: , for all ], such that , for all .
Theorem 2. Let be a nonexpansive map with . There exists then a nonexpansive mapping which selects , such that .
The obtained facts complete the investigation of these concepts started in E. Kemajou, H.-P. Künzi and O. O. Otafudu [Topology Appl. 159, No. 9, 2463–2475 (2012; Zbl 1245.54023)].