1 . 拓扑空间中满足一定条件的连续函数
,如果存在
,使得
,那么我们称函数
为“不动点”函数,而称
为该函数的一个不动点.在数学中,这被称为布劳威尔不动点定理,此定理得名于荷兰数学家鲁伊兹·布劳威尔(英语:L.E.J.Brouwer),是拓扑学里一个非常重要的不动点定理.现新定义:已知
为函数
的一个不动点,若
满足
,则称
为
的双重不动点.给出下列三个结论:
①
;
②
;
③
.
具有双重不动点的函数为是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3102c0a2f53b80f9dddbf9352537e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5980f861d6c2c86b41267ea1e3df2e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf0f8564284da0f7f8770f108590554.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4aef371b9d068de1fae531a96dd278d.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ae8fcec9459da808411feac6255e5f.png)
具有双重不动点的函数为是
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