GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS IN LOCALLY G-CONVEX SPACES

IntroductionLetX ,YbetwotopologicalspacesandZbeanonemptyset.LetF∶X×X→ 2 Z,A∶X→ 2 XandC∶X→ 2 Zbeset_valuedmappingswhere2 ZdenotesthefamilyofallsubsetsofZ .　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅰ ) (inshort,GVQEP(Ⅰ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 1 )　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅱ ) (inshort,GVQEP(Ⅱ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 2 )　　…     

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

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

SOME COINCIDENCE THEOREMS OF SET-VALUED MAPPINGS

Browder[1]obtained the sharpend forms of the Schauder fixed point theorem.Manyauthors generalized Browder’s results in several aspects.Recently,H.M.Ko and K.K.Tan[2,3]generalized Browder’s theorems to the coincidence theorems of set-valuedmappings.In this paper,we also show some coincidence theorems of set-valued mappings.They improve and generalize the important results in[1,2,3].     

GENERAL RANDOM FIXED POINT THEOREM AND ITS APPLICAT1ONS

In this paper, we obtain a general random fixed point theorem which generalizes the main results of Engle and Bocsan. The usefulness of this theorem seems to lie in the fact that unlike many random fixed point theorems obtained by using special methods can be proved by using out general theorem (Theorem 1 and Corollaries 1 and 2). Finally, we indicate some possible applications of our results to nonlinear random integral and differential equations.     

广义拟似变分不等式解的存在性*

本文在Hausdorff拓扑矢量空间的仿紧设置下对一类具有间断映象的广义拟似变分不等式证明了解的存在性定理.这些定理统一、改进和推广了广义拟变分不等式的许多最近结果.     

EQUILIBRIUM IN ABSTRACT ECONOMICS WITH A NON－COMPACT INFINITE DIMENSIONAL STRATEGY SPACE

ＥＱＵＩＬＩＢＲＩＵＭＩＮＡＢＳＴＲＡＣＴＥＣＯＮＯＭＩＣＳＷＩＴＨＡＮＯＮ－ＣＯＭＰＡＣＴＩＮＦＩＮＩＴＥＤＩＭＥＮＳＩＯＮＡＬＳＴＲＡＴＥＧＹＳＰＡＣＥＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｒｎａｌＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎ...     

随机积分和微分方程在弱拓扑下解的存在性和比较结果*

在本文中,我们对非线性随机Volterra积分方程在Banach空间的弱拓扑下的随机解证明了几个存在定理.然后作为应用,我们得到了随机微分方程的弱随机解的存在定理.还得到了这些随机方程的极值随机解的存在性和随机比较定理.我们的定理改进和推广了[4,5,10,11,12]中的相应结果.     

一类含非紧映象方程的正解

本文定义了从一个Banach空间的相对开子集到另一个Banach空间的A-proper映象的广义相对拓扑度并且引入了广义P-紧和P₁-紧概念.其次,我们证明了含这些映象的方程的正解存在性定理.我们的定理改进和推广了最近的一些结果.     

具有H-凸截口的非紧集的交定理及其应用

在本文内,我们推广了Ma,Fan,Tarafdar,Lassonde和Shih-Tan等作者关于具有凸截口集的交定理到没有线性结构的H-空间和非紧设置.同时给出了我们的定理对Vou Neumann型极小极大定理的应用.     

凸距离空间内星形子集非扩张型映射不动点*

在本文中.我们给出包含一个集合的某种星形集的刻划及其性质.然后利用这些刻划和性质讨论凸距离空间的星形子集上非扩张型映射的不动点的存在问题,推广了丁协平、Beg和Azam的某些最近结果.最后还给出一个例子说明以上推广是本质上的推广.