1) vectorial Caristi fixed point theorem
向量值Caristi不动点定理
1.
In this paper,we give a vectorial Ekeland variational principle with a w-distance,a vectorial Takahashi nonconvex minimization theorem with a w-distance and a vectorial Caristi fixed point theorem with a w-distance.
本文中,我们给出了带有w-距离的向量值Ekeland变分原理,带有w-距离的向量值Takahashi非凸极小化定理和带有w-距离的向量值Caristi不动点定理。
2) Caristi fixed point theorem
Caristi不动点定理
1.
We proved the set valued mapping is almost lower semicontinuous from the space made of bounded below function to the space made of the mapping that meets the conditions of Caristi fixed point theorem.
证明了从Caristi不动点定理中下半连续,下有界的泛函组成的空间到满足Caristi不动点定理条件的映射组成的空间的集值映射是几乎下半连续的。
2.
Anthor proved,there exists a equivalent metric d~*,under certain conditions,such that the mapping F which satisfies the condition of caristi fixed point theorem,is a Banach contraction mapping respect to d~*.
作者证明了在一定条件下存在某一等价度量d*,使得满足Caristi不动点定理条件的映射F关于d*是Banach压缩映射,因此,Caristi不动点定理在一定条件下与Banach压缩映射原理等价。
3.
Based on the equivalence property of Caristi fixed point theorem and Ekeland variation principle,we proved that ε-solutions of Ekeland variation principle are included in the set of fixed points of Caristi fixed point theorem.
在Ekeland变分原理和Caristi不动点定理等价的基础上,进一步证明了Ekeland变分原理中的ε-极值点包含在Caristi不动点定理中对应映射的不动点集中。
3) Caristi fixed point
Caristi不动点
1.
Research on sufficiency and necessary condition of Caristi fixed point theorem
Caristi不动点定理的充要条件
4) set valued Caristi type theorem
集值Caristi型定理
6) multivalued fixed point theorem
多值不动点定理
补充资料：Borel不动点定理
Borel不动点定理
Borel fixed - point theorem
B吮l不动点定理{B.限l五xe小州nt价e僻m二匆卿，T侧邓吧，f.01”聊叉B“狱班滋n卜.王j 设F为代数闭域kl二非空完全代数簇，正则地作用于犷上的连通可解代数群G(见变换的代数群扭1罗-braic goup of transformat一ons))在卜中有不动点.由这个定理可以推出代数群的B.耽l子群(Borel sub-grouP)是共扼的(Bore卜MOI洲)叉)B定理(Borel一Moro-zov theorem))，不动点定理是A.Borel([lj)证明的.Borel定理可以推广到任意域k(不一定代数封闭卜设F为在域k上定义的完全簇若连通可解k分裂群(人一sPlit grouP)G正则地作用在F上，则有理人点集V(k)或者为空集，或者它包含G的一个不动点.因此推广的Bore]子群共扼性定理是:若域k是完满的，则一个连通人定义的代数群H的极大连通可解北可裂子群，在H的k点构成的群中元素作用下互相共辘(f21)，
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参考词条