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1.
A new type of fixed point theorem in metric spaces   总被引:1,自引:0,他引:1  
We prove a generalization of Edelstein’s fixed point theorem. Though there are thousands of fixed point theorems in metric spaces, our theorem is a new type of theorem.  相似文献   

2.
In this paper, we first prove a generalized KKM theorem, and then use this generalized KKM theorem to establish the generalized equi-KKM theorem, common fixed point theorems for a family of multivalued maps, and the Kakutani-Fan-Glicksberg fixed point theorem. We also show that an existence theorem of the common fixed point theorem is equivalent to the Kakutani-Fan-Glicksberg fixed point theorem.  相似文献   

3.
引入了L-空间和L-空间上的KKM类映射,建立了关于该类映射的一些不动点定理,其中包括Schauder型和Fan-Browder型不动点定理.得到了L-空间中的KyFan匹配定理和叠合点定理.  相似文献   

4.
We give generalizations in complete gauge spaces of the following results: Bishop-Phelps’ theorem, Ekeland’s variational principle, Caristi’s fixed point theorem, the drop theorem and the flower petal theorem. We show that our generalizations are equivalent. We apply those results to obtain fixed point theorems for multivalued contractions defined on a closed subset of a complete gauge space and satisfying a generalized inwardness condition.  相似文献   

5.
We prove a fixed point theorem for a generalized weakly contractive mapping and a fixed point theorem for a pair of weakly contractive mappings. We also show that these mappings satisfy properties P and Q.  相似文献   

6.
The theory of countable partially ordered sets (posets) is developed within a weak subsystem of second order arithmetic. We within \(\mathsf {RCA_0}\) give definitions of notions of the countable order theory and present some statements of countable lattices equivalent to arithmetical comprehension axiom over \(\mathsf {RCA_0}\). Then we within \(\mathsf {RCA_0}\) give proofs of Knaster–Tarski fixed point theorem, Tarski–Kantorovitch fixed point theorem, Bourbaki–Witt fixed point theorem, and Abian–Brown maximal fixed point theorem for countable lattices or posets. We also give Reverse Mathematics results of the fixed point theory of countable posets; Abian–Brown least fixed point theorem, Davis’ converse for countable lattices, Markowski’s converse for countable posets, and arithmetical comprehension axiom are pairwise equivalent over \(\mathsf {RCA_0}\). Here the converses state that some fixed point properties characterize the completeness of the underlying spaces.  相似文献   

7.
We establish a new fixed point theorem for mappings satisfying a general contractive condition of integral type. The presented theorem generalizes the well known Ćirić’s fixed point theorem [Lj. B. Ćirić, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (26) (1971) 19-26]. Some examples and applications are given.  相似文献   

8.
We consider a two-dimensional time scale system of first order dynamic equations and establish some necessary and sufficient conditions for the existence of nonoscillatory solutions for the system using Knaster fixed point theorem, the Schauder fixed point theorem and the Schauder–Tychonoff fixed point theorem. We also provide examples to underline the main results of this article.  相似文献   

9.
利用H.Amann的一个不动点定理及锥拉伸锥压缩不动点定理讨论了一类Hammerstein型积分方程的正解,得到了一个五解定理.  相似文献   

10.
We define the infinite-dimensional simplex to be the closure of the convex hull of the standard basis vectors in R, and prove that this space has the fixed point property: any continuous function from the space into itself has a fixed point. Our proof is constructive, in the sense that it can be used to find an approximate fixed point; the proof relies on elementary analysis and Sperner's lemma. The fixed point theorem is shown to imply Schauder's fixed point theorem on infinite-dimensional compact convex subsets of normed spaces.  相似文献   

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