锥度量空间中c-距离下的不动点定理

在锥度量空间中,用压缩性函数代替具体实数,获得了c-距离下的映射的新的不动点定理.所得结果在条件上不要求映射的非减性,且第一个定理去掉了锥的正规性,第二个定理去掉了映射的连续性,改进了原有的许多重要结论,并给出了相应的例子.     

Common coupled fixed point theorems in cone metric spaces for w-compatible mappings

In this paper we introduce the concept of a w-compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone having non-empty interior. Coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend and unify several well known comparable results in the literature. Results are supported by three examples.     

New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras

In this work, some new fixed point results for generalized Lipschitz mappings on generalized $c$-distance in cone $b$-metric spaces over Banach algebras are obtained, not acquiring the condition that the underlying cone should be normal or the mappings should be continuous. Furthermore, the existence and the uniqueness of the fixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examples and an application are given to support our new results.     

锥b-度量空间上映射的公共不动点定理

本文研究了锥b-度量空间上四个自映射的公共不动点问题.利用序列逼近的方法,获得了锥b-度量空间上四个自映射的一些公共不动点结果,将锥度量空间中的几个相关结果推广到锥b-度量空间中,并且给出了一个例子以支撑我们的结果.     

KKM mappings in metric type spaces

In this work we discuss some recent results about KKM mappings in cone metric spaces. We also discuss the fixed point existence results of multivalued mappings defined on such metric spaces. In particular we show that most of the new results are merely copies of the classical ones and do not necessitate the underlying Banach space nor the associated cone.     

非锥映射的不动点指数计算及其应用

本文应用锥理论获得了一类不是锥映射的非线性算子不动点指数计算的若干结果,并将所得结果应用于非线性椭圆型偏微分方程边值问题.     

向量值映射锥鞍点存在定理

本文首次通过借助Kakutani-Fan-Glicksberg固定点定理和非线性标量化,研究了向量值映射的Benson锥鞍点定理.然后,通过使用该Kakutani-Fan-Glicksberg固定点定理,同样得到了集值映射的锥松鞍点定理.     

锥b-Banach空间上非扩张映射的不动点定理

在锥b-Banach空间上考虑多个映射的公共不动点问题,利用Mann迭代法以及锥b-范数的条件下证明锥b-Banach空间上多个映射的公共不动点的存在性.     

Minimax Problems for Set-Valued Mappings

In this article, by virtue of the Fan-Browder fixed point theorem, we first obtain a minimax theorem and establish an equivalent relationship between the minimax theorem and a cone saddle point theorem for scalar set-valued mappings. Then, by using scalarization functions, we investigate an existence theorem of the cone saddle point for set-valued mappings. Simultaneously, we also establish a minimax theorem for set-valued mappings.     

Nonlinear Perturbations of Polyhedral Normal Cone Mappings and Affine Variational Inequalities

This paper establishes an upper estimate for the Fréchet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumption on the normal vectors of the active constraints at the point in question, the result leads to an upper estimate for values of the Mordukhovich coderivative of such mappings. On the basis, new results on solution stability of parametric affine variational inequalities under nonlinear perturbations are derived.     

关于非扩张映象的耗散扰动问题

研究非扩张映象的耗散扰动问题。并把所得结果应用于研究某些类型的非线性积分方程解的存在性。     

Cone metric spaces and fixed point theorems in diametrically contractive mappings

In this paper, some topological concepts and definitions are generalized to cone metric spaces. It is proved that every cone metric space is first countable topological space and that sequentially compact subsets axe compact. Also, we define diametrically contractive mappings and asymptotically diametrically contractive mappings on cone metric spaces to obtain some fixed point theorems by assuming that our cone is strongly minihedral.     

Fixed Points of a φ-G-Contractive Mapping with Respect to a c-Distance on an Abstract Metric Space Endowed with a Graph

Mathematical Notes - In this paper, we prove the existence of fixed points for any mapping that is a Banach G-contraction with respect to a c-distance on a cone metric space endowed with a graph.     

序锥度量空间中涉及距离改变函数的拟压缩的公共不动点结果（英文）

Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.     

Denjoy-Wolff theorems for Hilbert’s and Thompson’s metric spaces

We study the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert’s metric or Thompson’s metric. We establish several Denjoy-Wolff type theorems which confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We also extend and put into a broader perspective results by Gaubert and Vigeral concerning the linear escape rate of such nonexpansive mappings.     

拓扑向量空间中锥半连续性与锥拟凸映射

对于拓扑向量空间中的几个锥拟凸映射,讨论了它们之间的若干关系,同时,对锥半连续及锥上半连续映射的锥拟凸性给出了一些结果。     

Some results of Perov type in rectangular cone metric spaces

In 2000, Branciari replaced the triangle inequality by a more general one which today is known as the rectangular inequality and introduced the notion of generalized metric space or rectangular metric space. Subsequently Azam, Arshad, and Beg introduced the concept of rectangular cone metric space and proved fixed point results for Banach-type contractions in rectangular cone metric spaces. In this paper, we establish fixed point results for mappings that satisfy a contractive condition of Perov type in rectangular cone metric spaces.     

零点不可导时锥映射的歧点与正特征元的全局结构

研究了半序Banach空间中一类非线性锥映射歧点的存在性与正特征元的全局结构.与已知文献不同的是,不要求算子在零点沿着锥Frechet可微. 作为应用,讨论了一类椭圆型偏微分方程边值问题正解的歧点与全局结构.     

赋值Banach代数的偏序D^-度量空间和公共不动点定理

基于完备的D^*-度量空间,提出具有Banach代数的偏序D^*-度量空间的定义,通过迭代序列的构造,证明了新定义下不动点定理的存在性及唯一性理论.随后引入了关于两个连续自映射的公共不动点定理,并对其存在性和唯一性进行了研究.所得结果推广了现有文献.     

实Banach空间中锥上的随机逼近和随机不动点定理

本文在实Ｂａｎａｃｈ空间的锥上证明了集值映射的随机逼近定理．作为应用，讨论了几个随机的不动点定理．我们的工作推广了Ｌｉｎ，Ｓｅｈｇａｌ和Ｓｉｎｇｈ的结果．