共查询到20条相似文献,搜索用时 15 毫秒
1.
The present paper is divided into two parts. In the first part, we derive a Fan-KKM type theorem and establish some Fan type geometric properties of convex spaces. By applying our results, we also obtain some coincidence theorems and fixed-point theorems in the setting of convex spaces. The second part deals with the applications of our coincidence theorem to establish some existence results for a solution to the generalized vector equilibrium problems. 相似文献
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Xie Ping DING 《数学学报(英文版)》2006,22(5):1529-1538
A new class of locally finite continuous topological spaces (for short, locally FC-spaces) and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures. 相似文献
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Petru Cojuhari 《Journal of Mathematical Analysis and Applications》2005,304(2):584-598
We introduce the notion of induced Hilbert spaces for positive unbounded operators and show that the energy spaces associated to several classical boundary value problems for partial differential operators are relevant examples of this type. The main result is a generalization of the Krein-Reid lifting theorem to this unbounded case and we indicate how it provides estimates of the spectra of operators with respect to energy spaces. 相似文献
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主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性. 相似文献
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In this paper we first introduce the concept of compatible mappings of type (B) and compare these mappings with compatible mappings and compatible mappings of type (A) in Saks spaces. In the sequel, we derive some relations between these mappings. Secondly, we prove a coincidence point theorem and common fixed point theorem for compatible mappings of type (B) in Saks spaces. 相似文献
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Xie Ping Ding 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1834-1841
In this paper, by using a fixed point theorem for expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces due to the author, we first prove a collective fixed point theorem and an existence theorem of equilibrium points for a generalized game. As applications, some new existence theorems of solutions for systems of generalized quasi-variational inclusion problems are established in noncompact topological spaces. Our results are different from known results in the literature. 相似文献
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在Fréchet空间中利用推广的Tychonov不动点定理研究了Banach空间中一阶非线性微分方程终值问题解的存在性. 相似文献
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Necessary conditions of the multiplier rule type for vector optimization problems in Banach spaces are proved by using separation theorems and Ljusternik's theorem. The Pontryagin maximum principle for multiobjective control problems with state constraints is derived from these general conditions. The paper extends to vector optimization results established in the scalar case by Ioffe and Tihomirov. 相似文献
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本文利用Monch不动点定理和一个比较结果,研究了实 Banach空间中二阶非线性混合型脉冲积分-微分方程初值问题解的存在性. 相似文献
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丁协平 《应用泛函分析学报》2010,12(4):289-304
在局部FC-一致空间内引入和研究了某些新的联立广义矢量拟平衡问题组和具有联立广义矢量拟平衡组约束的数学规划.应用作者在局部FC-一致空间得到的Himmelberg型不动点定理,首先在局部FC-一致空间内对联立广义矢量拟平衡问题组的解证明了某些新的存在性定理.作为应用,对具有联立广义矢量拟平衡组约束的数学规划的解得到了某些新的存在性定理. 相似文献
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Motivated by the Suzuki’s type fixed point theorems, we give several new existence theorems for scalar quasi-equilibrium problems, and vector quasi-equilibrium problem on complete metric spaces. We give important examples for our results. Note that the solution of quasi-equilibrium problem (resp. vector quasi-equilibrium problem) is unique under suitable conditions, and we can find the unique solution by the Picard iteration. Besides, we also give a new coincidence theorem on complete metric spaces. Finally, we give a new minimax theorem on complete metric spaces. Note that the solution of minimax theorem is unique under suitable conditions, and we can find the unique solution by the Picard iteration. 相似文献
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Xie-Ping Ding Jen-Chih Yao Lai-Jiu Lin 《Journal of Mathematical Analysis and Applications》2004,298(2):398-410
In this paper we establish a collectively fixed point theorem and an equilibrium existence theorem for generalized games in product locally G-convex uniform spaces. As applications, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are derived in product locally G-convex uniform spaces. These theorems are new and generalize some known results in the literature. 相似文献
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一般化凸空间上的截口定理和变分不等式定理 总被引:3,自引:0,他引:3
摘要:本文利用Brouwer不动点定理或已知的KKM型定理,得到一般化凸空间上的截口定理.讨论了变分不等式解的存在性问题。对文中的相应结论进行了一般化和改进。 相似文献
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In this paper, we introduce and study a class of implicit vector equilibrium problems, which includes a number of (scalar) implicit equilibrium problems, implicit variational inequalities, and implicit complementarity problems as special cases. By using KKM-Fan theorem, we prove some new existence theorems of solutions for this kind of implicit vector equilibrium problems in Hausdorff topological vector spaces. Our results extend and unify some corresponding results of several authors. 相似文献
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Xie Ping DING 《数学学报(英文版)》2007,23(10):1869-1880
In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature. 相似文献
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考虑一类隐式形式多值向量均衡问题的解的存在性,该类问题包含了多值均衡问题、隐式向量均衡问题、多值变分不等式问题、向量变分不等式问题以及向量互补问题作为其特殊情形.利用广义Fan-Browder不动点定理,得到了拓扑向量空间中该类问题解的存要性定理,该结果推广并统一了已有问题解的存在性结果. 相似文献