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| RESEARCH ANNOUNCEMENTS On a Problem Given by D.R.Smart | |
| 作者姓名： | 娄本东 张志涛 |
| 作者单位： | Shandong University，Jinan，250100，Shandong，Shandong University，Jinan，250100，Shandong |
| 摘 要： | In 1] Section 5.2, D.R. Smart gave a problem: Does every shrinking mappingof the closed unit ball in a Banach space have a fixed point? In this paper, we givea negative answer to this problem by constructing a counter-example. Definition Let (X,d) be a metric space and T a mapping of X into X. Wecall T a shrinking mapping if d(Tx,Tg) |
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