Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

L-超空间上的几乎连续集值映射

本文在L-超空间上引入L集值映射的上(下)几乎连续性及几乎连续性等概念，得到其若干等价条件，并研究了几乎连续集值映射与连续集值映射之间的关系．     

关于Ls优化映象的极大元存在定理

给出了Ls类映象和Ls优化映象的概念，在G-凸空间中建立了关于Ls类映象和Ls优化映象的极大元存在定理，作为应用，给出了G-凸空间中的极大极小不等式。     

关于广义L-S-KKM映象的性质

作为研究非线性领域中很多问题的重要工具，Lin和Chang引入了一类S-KKM映象，证明了若干S-KKM映象的性质．本文在L-凸空间中建立了广义L-S-KKM映象，讨论了广义L-S-KKM映象的性质，并且证明了L-S-KKM集族是KKM集族的真推广．作为应用还得到了L-凸空间中的一个不动点定理．改进和推广了广义S-KKM映象的相关性质．     

仿紧集上的广义双拟变分不等式

利用关于仿紧集上的单位分解定理，将紧集上的广义双拟变分不等式解的存在性定理推广到仿紧集情形。     

MENGER概率度量空间中集值映象序列的混合不动点

本文在Ｍｅｎｇｅｒ概率度量空间中提出混合不动点概念，研究了集值映象序列的公共混合不动点定理，所得结果改进和推广了近期相关的重要结果。     

一个收缩映像不动点定理与Banach不动点定理的等价性

由一个收缩映像的不动点定理导出Ｂａｎａｃｈ压缩映像原理，并证明了在局部紧的度量空间中，这个不动点定理与Ｂａｎａｃｈ压缩映像原理在本质上是等价的     

L-凸空间中的Ky Fan极大极小不等式及其应用

在较弱的条件下证明了L-凸空间中的Ky Fan极大极小不等式，并给出其等价形式．作为应用，得出了L-凸空间中的鞍点定理。     

Extended radial epiderivatives of non-convex vector-valued maps and parametric quasiconvex programming

In this paper, we consider extended vector-valued mappings defined on a normed linear space. Based on the recent semicontinuous regularizations related to hypographical and/or epigraphical profile mappings of the considered function introduced, we define semicontinuous radial epiderivatives. We, then, demonstrate that the properties of these epiderivatives amount to properties of hypographical and/or epigraphical profile mappings of the corresponding difference quotient of the underlying function, which simplify fairly well the proofs in the radial epiderivative formulaes. In particular, we stress the impact of semicontinuity, hence, we characterize with new arguments the radial epiderivatives in terms of the suprema and/or infima of the interiorly radial cone of the hypograph and/or epigraph of the considered function. Finally, we obtain optimality conditions for general non-convex constrained vector optimization problems. We apply thereafter the obtained pattern to a parametric quasiconvex programming problem for which we derive necessary and sufficient optimality conditions that are not sensitive to perturbation at the nominal level, yielding henceforth more – and strong at least under asymptotically regular constraints – information than the recent stability results obtained under additional conditions on the regularity of the normal cone to the adjusted sublevel sets of the underlying function.     

Φ-φ-型压缩映象不动点的存在性

使用压缩尺度函数,在完备2-距离空间中研究一类Φ-φ-型轨道压缩映象不动点的存在与唯一性,在适当条件下证明了一个新的不动点定理,推广和改进了已知的结果.