Lyusternik-Graves theorem and fixed points
Lyusternik-Graves theorem and fixed points
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DOI：
10.1090/s0002-9939-2010-10490-2
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发表时间：
2011-02
期刊：
影响因子：
--
通讯作者：
A. Dontchev;H. Frankowska
中科院分区：
文献类型：
--
作者：
A. Dontchev;H. Frankowska
对于作用于度量空间中的集值映射，我们给出了以下一般范式的局部和全局版本，它源于Lyusternik-Graves定理和收缩原理：如果是具有常数的度量正则，并且是具有常数的Aubin （Lipschitz）连续，则到的不动点集合的距离由与之间的最小距离的乘界。从这个结果我们得到了已知的Lyusternik-Graves定理，Arutyunov最近的一个定理，以及一些不动点定理。
For set-valued mappings and acting in metric spaces, we present local and global versions of the following general paradigm which has roots in the Lyusternik-Graves theorem and the contraction principle: if is metrically regular with constant and is Aubin (Lipschitz) continuous with constant such that , then the distance from to the set of fixed points of is bounded by times the infimum distance between and . From this result we derive known Lyusternik-Graves theorems, a recent theorem by Arutyunov, as well as some fixed point theorems.