摘要
完备内积空间中有界闭凸集的非扩张自映射有不动点。概率度量空间的非扩张自映射也有类似的不动点定理。完备变内积空间中,变内积引导出一个普通内积,作为内积空间和概率度量空间,上述结论显然是成立的。但变内积空间关于概率范数的非扩张自映射是否也有不动点呢?在本文中,我们证明了,若 B 是完备变内积空间 H 的紧凸集,T 是从 B 到 B的非扩张映射,I-T 是单调映射,则 T 有不动点,而且 T 的不动点组成的集合是凸集。
On bounded closed convex subset of complete inner product space nonexpansive itself mapping possesses fixed point.Probabilistie metric space has also similar theorem.In complete variant inner product space,variant inner product induced a ge- neral inner product.Of course there are above-mentioned conclusions as inner product space and psobabilistic metric space,but for nonexpansive mapping of probabilitstic norm,is there fixed point in complete variant inner product space?in this paper,we proved that suppose B is a compact convex subset of real complete variant product space Q∈B,T is a nonexpapsive mapping from B to B,I—T is a monotone mapping,the mapping T possesses fixed point and set of fixed points for T is convex.
出处
《重庆邮电学院学报（自然科学版）》
1989年第1期68-72,共5页
Journal of Chongqing University of Posts and Telecommunications(Natural Sciences Edition)
关键词
变内积空间
非扩张映射
不动点
variant innet product space
complete
compact convex set
nonexpansive mapping
fixed point
