Generalized Strongly Nonlinear Quasi-Complementarity Problems

ＧＥＮＥＲＡＬＩＺＥＤＳＴＲＯＮＧＬＹＮＯＮＬＩＮＥＡＲＱＵＡＳＩ－ＣＯＭＰＬＥＭＥＮＴＡＲＩＴＹＰＲＯＢＬＥＭＳＬｉＨｏｎｇ－ｍｅｉ（李红梅）ＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ），Ｃｈｅｎｇｄｕ（Ｒｅ...     

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．     

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.     

Random directional contractors and their applications

In this paper, as the generalizations of Altman’s directional contractors[4,5] and Lee and Padgett’s random contractors[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.     

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。     

随机积分方程和微分方程解的存在性和比较结果

本文是[1]的继续.在本文中我们对非线性随机Volterra积分方程给出了解的另一存在性准则,极值解的存在性定理和随机积分不等式的比较定理,这些定理分别推广了Vaughan[2,3]和Lakshmikantham[4,5]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.