多值映射的公共随机不动点定理

在本文中,我们对一般集值压缩型映射证明了几个随机公共不动点定理,这些定理改进和推广了[1～18]中的相应结果。     

集值映象的某些重合定理

Browder[1]已得到了Schauder不动点定理的加强形式.许多作者从不同方向推广了Browder的结果.最近H.M.Ko;K.K.Tan[2]在放松紧性条件下得到了Browder定理的改进,K.K.Tan[3]将Browder定理推广到了集值映象对的重合定理,在本文中我们得到了集值映象对的某些重合定理,它们分别改进和推广了[1,2,3]中主要结果.     

Quasi-variational inequalities and social equilibrium

A quasi-variational inequality is proved in paracompact setting which generalizes theresults of Zhou Chen and Aubin.As applications,two existence theorems on the solutions ofoptimization problems and social equilibria ofmetagames are showed which improve andextend the recent results of Kaczynski-Zeidan and Aubin.     

拟变分不等式和社会平衡

我们在仿紧设置下,在Hausdorff拓扑矢量空间内证明了一个广义拟变分不等式,推广了Zhou-Chen和Aubin的相应结果.作为应用,关于最优化问题的解和亚对策的社会平衡解的两个存在性定理被证明.这些定理改进和推广了Kaczynki-Zeidan和Aubin的最近结果.     

Behavior of solution set for bilevel generalized mixed equilibrium problems in topological vector spaces

A new bilevel generalized mixed equilibrium problem （BGMEF） is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field.     

Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium

A new system of generalized mixed implicit equilibrium problems(SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces.First,an auxiliary mixed equilibrium problem(AMEP) is introduced.The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions.Next,by using the solution mapping of the AMEP,a system of generalized equation problems(SGEP) is considered,and its equivalence with the SGMIEP is shown.By using the SGEP,a new iterative algorithm for solving the SGMIEP is proposed and analyzed.The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions.These results are new,which unify and generalize some recent results in this field.     

COINCIDENCE THEOREMS INVOKING COMPOSITES OF ACYCLIC MAPPINGS AND APPLICATIONS

1IntroductionRecentlytherehaveappearedanumberofnewfixedpointtheoremsandcoincidencetheorexnsinvolvingsthcalledKakutanifactorizablemultifunctionsorcompositesofacyclicset-valuedmappingsdefinedonconvexsubsetsoftopologicalvectorspaces;forexample,see[1-3].Intheseresults,authorsassumethateitherthedoesnOfmappingiscompact,orthemappillgiscompact.Inthispaper,wefirstprovesomeverygeneralcoincidencetheoremsinvolvingtheclassVJofset-valuedmappings"lidernoncompactsettingwhichgeneralizesTheoremIofPark,Singha…     

随机定向收缩及其应用*

作为Altman的定向收缩理论[4,5]和Lee,Padgett的随机收缩理论[1,2]的推广,本文对非线性集值随机算子引入了随机定向收缩概念,利用这一新概念和超限归纳法,我们证明了非线性集值随机算子方程随机解的几个存在性定理.这些定理分别改进和推广了[1,2,4,5,11]中相应的结果.其次,给出了我们的结果对非线性随机积分和微分方程的某些应用.     

随机积分和微分方程解的存在性准则

在[1]中我们已证明了一个一般的随机不动点定理并给出了某些应用,在本文中我们将给出该结果的进一步应用.首先证明了一随机Darbo不动点定理,然后利用此定理在紧性假设下给出了非线性随机Volterra积分方程和非线性随机微分方程Cauchy问题随机解的存在性准则.我们的定理改进和推广了Lakshmikantham[3,4],Vaugham[2],De Blasi和Myjak[5]等人的结果.     

没有紧性, 连续性和凹性的多准则对策的帕雷多平衡*

在本文中利用作者得到的一极小极大不等式,对不具有紧性,连续性和四性的多准则对策在拓扑矢量空间和自反Banach空间内证明了某些帕雷多平衡存在定理。