摘要
1974年,Lim给出了一致凸Banach空间上非扩张集值映射的不动点定理,同时提出问题:该定理在有正规结构的Banach空间中是否成立? 1989年,断言解决了这一问题。然而一年之后,用反例说明,的证明有本质错误。本文证明:在适当的条件下,该问题的答案是肯定的。
In 1974, Lim proved a fixed point theorem for set-valued mappings on uniformly convex Banach spaces and asked if the assertion held for Banach spaces with normal structure. In 1989, Xie Jipei annouced that the answer was positive. But unfortunately, his proof was incorrect. In this paper, we show that under some condition, the answer is positive.
出处
《哈尔滨师范大学自然科学学报》
CAS
1994年第1期1-3,共3页
Natural Science Journal of Harbin Normal University
关键词
正规结构
集值映象
不动点
Nonexpansive set-valued mapping
Normal structure
Quasivanable
