一致凸度量线性空间的自反性及其应用

Reflexivity of Uniform Convexity Metric Linear Spaces and Its Applications

为研究度量线性空间中凸集的逼近性质，Ｇ．Ｃ．Ａｈｕｊａ等引进了度量线性空间的严格凸性及一致凸性的定义。本文证明了完备的一致凸的度量线性空间是自反的。同时，作为应用，研究了最佳联合逼近元的存在性与唯一性问题。

In order to study the approximation properties of convex set in metric linear spaces,G.C.Ahuja and others introduced the notions of strict convexity and uniform convexity in metric linear space. In this paper it is proved that uniform convexity metric linear spaces with completeness are reflexive. As applications,exis-tence and uniqueness of a best simultaneous approximation element are studied.