A fixed-point principle
A fixed-point principle
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DOI：
10.1007/bf01076087
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发表时间：
1967
影响因子：
0.4
通讯作者：
B. N. Sadovskii
中科院分区：
文献类型：
--
作者：
B. N. Sadovskii
I（K）= K。(3)证据如果x T，则序列{fn（x）; n= 0，1，2，.}是有界的，并且由算子f映射到序列{fn（x）; n= 1，2....}，它的非紧性度量等于原始序列的非紧性度量。从这一点和凝聚算子的定义可以得出序列{fn（x）}在E中是紧的。我们用K表示它的所有极限点的集合。如果是，则y=。limfnk（x）.另一方面，对于给定的点y，我们可以找到一个点z EK：
I (K)= K.(3) proof. If x T, the sequence {fn (x); n= 0, 1, 2,...} is bounded and is mapped by the operator f into the sequence,{fn (x); n= 1, 2....}, whose measure of noncompactness is equal to the measure of noncompactness of the original sequence. From this and from the definition of a condensing operator it follows that the sequence {fn (x)} is compact in E. We denote by K the set of all its limit points. If YE K, so that y=. limfnk (x). On the other hand, for a given point y we can find a point z EK: