CRITERIA FOR THE EXISTENCE OF SOLUTIONS TO RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS

In[1],we proved a general random fixed point theorem and gave some applications.Inthis paper,we shall give further applications of the theorem.We first obtain a randomDarbo’s fixed point theorem,using the theorem,we give the criteria for the existence ofsolutions under compactness hypotheses to nonlinear random volterra integral equationsand the Cauchy problem of nonlinear random differential equations.Our theorems improveand generalize some main results of Lakshmikanthem,Vaughn as well as De Blasiand Myjak.     

局部FC-一致空间内的广义约束多目标对策

在没有任何凸性结构的局部FC-一致空间内引入和研究了一类新的广义约束多目标对策,其中局中人数可以是有限或无限的和所有的支付函数可以取值于无限维空间．利用在局部FC-一致空间内得到的一个Himmelberg型不动点定理,在局部FC-一致空间内对广义约束多目标对策建立了某些弱Pareto平衡存在性定理．这些定理改进,统一和推广了最近文献中相应结果．     

广义凸空间内的拟平衡问题和约束多目标对策

在没有线性结构的广义凸空间内研究了一类拟平衡问题和一类约束多目标对策.首先在非紧广义凸空间内对拟平衡问题证明了两个解的存在性定理.然后作为拟平衡存在定理的应用,在广义凸空间内对约束多目标对策建立了几个加权Nash-平衡和帕雷多平衡存在定理.这些定理改进、统一和推广了最近文献中多目标对策的相应结果.     

局部FC-一致空间内凝聚映象的极大元和广义对策及应用(Ⅱ)

在局部FC-一致空间内,引入和研究了某些新的涉及凝聚集值映象的广义矢量拟平衡问题组．应用作者在文(Ⅰ)中对局部FC-一致空间内的凝聚集值映象得到的极大元存在性定理,在局部FC-一致空间内,对这些广义矢量拟平衡问题组的解,证明了某些新的存在性定理．这些结果改进和推广了文献中某些已知结果到局部FC-一致空间．     

Banach空间内一类广义混合隐平衡问题组解的存在性和迭代算法

在Banach空间内引入和研究了一类新的广义混合隐平衡问题组．首先,对广义混合隐平衡问题组引入了Yosida逼近映射概念．利用此概念,考虑了一个广义方程问题组并证明了它与广义混合隐平衡问题组的等价性．其次,应用广义方程问题组,建议和分析了计算广义混合隐平衡问题组的近似解的迭代算法．在相当温和的条件下,证明了由算法生成的迭代序列的强收敛性．这些结果是新的并且统一和推广了这一领域内的某些最近结果．     

New collectively fixed point theorems and applications inG-convex spaces

By applying the technique of continuous partition of unity and Tychonoff’s fixed point theorem, some new collectively fixed point theorems for a family of set-valued mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G-convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence theorems of abstract economies are also obtained in G-convex spaces. Our theorems improve, unify and generalized many important known results in recent literature.     

求解广义混合隐拟平衡问题的预测修正算法

引入和研究了一类新的具有四元函数的广义混合隐拟平衡问题．这类平衡问题包含了很多已知的广义平衡问题和广义混合隐拟变分不等式问题作为很特殊的情形．利用辅助原理技巧建议和分析了求解广义混合隐拟平衡问题的预测修正迭代算法．所建议算法的收敛性仅需要映象的连续性和部分松弛强单调性．     

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅱ)

By applying coincidence theorems in part ( Ⅰ ) for two families of setvalued mappings defined on product space of noncompact FC-spaces in preceding paper, some new existence theorems for system of vector equilibrium problems, system ofinequalities and system of minimax theorems were established in FC-spaces. These results generalize some known results in recent literature.     

乘积拓扑空间内的重合点组定理及应用(Ⅰ)

首先引入了无凸性结构的有限连续拓扑空间(简称FC-空间)新概念．其次在FC-空间内建立了一个新的连续选择定理．应用此定理,在很弱的假设下,对定义在非紧FC-空间的乘积空间上的两个集值映射簇证明了某些新的重合点定理．这些结果推广了最近文献中的许多已知结果．某些应用将在后继文章中给出．     

Solutions for a system of nonlinear random integral and differential equations under weak topology

I.IntroductionTheexistenceandcomparisonresultsofsolutionsfornonlinearVolterraintegralequationsinstrongtopologyofBanachspaceshavebeenobtainedbyVaughnI"'"],LakshmikanthamIl3]andLakshmikantham-Leela114l.TheexistenceresultsofweaksolutionsfortheCauchyproblemof…