Nonexpansive retractions in hyperconvex spaces
This article deals with nonexpansive retractions on a hyperconvex subsets \(D\) of a hyperconvex metric space \(M\). The authors investigate the problems of existence of retractions \(R\) of \(M\) onto \(D\) with the property \(R(M\setminus D)\subseteq\partial D\) or \(d(x,R(x))= \text{dist}(x,D)\) \((x\in M)\). In particular, they prove that a externally hyperconvex relative to \(M\) in some weak sense subset \(D\) with an empty interior a nonexpansive retraction of \(M\) such that \(R(M\setminus D)\subseteq\partial D\) and that for any compact weakly externally hyperconvex subset \(D\) there exists a nonexpansive retraction \(R\) of \(M\) onto \(M\) such that \(d(x,R(x))= \text{dist}(x,D)\) \((x\in M)\).
scientific article; zbMATH DE number 1556932
scientific article