Nonexpansive retractions in hyperconvex spaces

[摘要] This paper is primarily concerned with the study of conditions on a hyperconvex subset D of a hyperconvex metric space M which assure that there exists a nonexpansive retraction R of M\D onto D which has the property that R(M\D) subset of partial derivativeD. A related question we take up is, when is such a retraction R proximinal, that is, when does R have the property d(x, R(X)) = dist (x, D) for each x is an element of M? Among other things, we show that if a subset D of a hyperconvex metric space M has nonempty interior and is externally hyperconvex relative to M in a very weak sense, then there always exists a nonexpansive retraction of M onto D which maps M\D onto partial derivativeD. We also show that any compact weakly externally hyperconvex subset of a hyperconvex M is a proximinal nonexpansive retract of M. (C) 2000 Academic Press.

[发布日期] 2000-11-15