Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications

In this paper, we presented new and important existence theorems of solution for quasi-equilibrium problems, and we show the uniqueness of its solution which is also a fixed point of some mapping. We also show that this unique solution can be obtained by Picard’s iteration method. We also get new minimax theorem, and existence theorems for common solution of fixed point and optimization problem on complete metric spaces. Our results are different from any existence theorems for quasi-equilibrium problems and minimax theorems in the literatures.     

A minimax theorem for functions with possibly nonconnected intersections of sublevel sets

We apply the selection theorem for multivalued mappings with paraconvex values (rather than various versions of KKM-principle) to prove several minimax theorems. In contrast with well-known minimax theorems for coordinatewise semicontinuous functions, in our theorems finite intersections of sublevel or uplevel sets can be nonempty and nonconnected.     

Some alternative principles and mixed minimax theorems involving two functions

Some alternative principles and quantitative-topological minimax theorems involving two functions are given. Consequently, Geraghty–Lin's minimax theorem and Terkelsen's minimax theorem are generalized. This revised version was published online in June 2006 with corrections to the Cover Date.     

Two-function upward-downward minimax theorems

Two-function upward-downward minimax theorems are derived which contain Simons upward-downward minimax theorem as well as Domokos minimax theorem as special cases. Here the convexity assumptions on two functions are given by mixing up their values as means proposed by Lin and Quan.     

MINIMAX THEOREMS FOR SUBCONVEXLIKEFUNCTIONS WITH APPLICATIONS TO SADDLEPOINT PROBLEMS

1 IntroductionIt is well known that alternative theorenis and ntinimax tlleorenis fOr inequality systenismore or less liwo1ve sonle couvekity in their assun1Ptions(Refs. l-7). Generally convekity of afunctiou is related to certain couveXity of some set (Ref.&9). In this paper sonle new nAnmaxtl1eorems for bifunctions are obtailled. Tliese results are applied to derive saddle point tl1eorenis(Refs 10-13).In this paper we assume that X,Y Z and W are real locally collvex topological vectorsp…     

Some New Types of KKM Theorem in H spaces with Applications

本文证明了Ｈ－空中的几个新型非空交定理．作为应用,文中得到了向量值极大极小定理和不动点定理,并研究了抽象经济平衡问题．     

一个新的极大极小定理及应用

本文得到一个新的极大极小定理及其几个等价形式．作为这一结果的应用，我们得到区间空间上的Ｋｙ Ｆａｎ型截口定理，匹配定理和几个集值映象的不动点定理．     

Minimax Theorems with Bregman Distance in Banach Spaces

Since Bregman distance is a generalized distance function which does not satisfy the triangle inequality nor symmetry, it is important to study minimax theorems in reflexive Banach spaces. Our minimax theorems differ from those in previous literature.     

Some fixed-point theorems and minimax inequalities in FC-space

By applying the existence theorem of maximal elements, some new collectively fixed-point theorems for a family of set-valued mappings defined on the product space of noncompact FC-space are proved and some new theorems about minimax inequality involving two functions are given to show the relations of fixed-point theorem and minimax inequality in FC-spaces. These results improve and generalize many important results in the recent literature.     

关于极小极大原理

通过减弱条件,获得了一个新的结果。由此,我们给出一些新的极小极大定理和极小极大不等式。     

Ky Fan极大极小不等式在H-空间的进一步推广和应用

本文在Ｈ－空间得到一个新的ｍｉｎｉｍａｘ不等式,并得到了与其等价的几何形式、极大元存在定理及作为其应用的不动点定理。     

Second order duality for nondifferentiable minimax programming problems with generalized convexity

In this paper, we are concerned with a class of nondifferentiable minimax programming problem and its two types of second order dual models. Weak, strong and strict converse duality theorems from a view point of generalized convexity are established. Our study naturally unifies and extends some previously known results on minimax programming.     

几个拓扑型极大极小定理

我们证明了几个新的拓扑型极大极小定理，我们的结果推广了[5]中的相应结论。     

Equilibrium existence theorems in KKM spaces

An abstract convex space satisfying the KKM principle is called a KKM space. This class of spaces contains G$G$-convex spaces properly. In this work, we show that a large number of results in KKM theory on G$G$-convex spaces also hold on KKM spaces. Examples of such results are theorems of Sperner and Alexandroff–Pasynkoff, Fan–Browder type fixed point theorems, Horvath type fixed point theorems, Ky Fan type minimax inequalities, variational inequalities, von Neumann type minimax theorems, Nash type equilibrium theorems, and Himmelberg type fixed point theorems.     

Fixed point theorems for better admissible multimaps on almost convex sets

We obtain new fixed point theorems on multimaps in the class Bp defined on almost convex subsets of topological vector spaces. Our main results are applied to deduce various fixed point theorems, coincidence theorems, almost fixed point theorems, intersection theorems, and minimax theorems. Consequently, our new results generalize well-known works of Kakutani, Fan, Browder, Himmelberg, Lassonde, and others.     

Coincidence Theorems with Applications to Minimax Inequalities, Section Theorem, Best Approximation and Multiobjective Games in Topological Spaces

Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.     

Generalized KKM theorems on hyperconvex metric spaces and some applications

In this work, we establish the intersection property for a family of admissible subsets in a hyperconvex metric space, and we apply this intersection property to get generalized KKM theorems, coincidence theorems, variational inequality theorems and minimax inequality theorems.     

Coincidence theorems and minimax theorems

In the present paper a few coincidence theorems and minimax theorems are given so as to unify and strengthen the corresponding results in [3], [4] and [5].The Project Supported by National Natural Science Foundation of China.     

System of coincidence theorems with applications

In this paper, we establish systems of coincidence theorems from which solution of system of inequalities and system of minimax theorems was established in this paper.     

广义凸空间内的KKM型定理和极小极大不等式及鞍点定理

本文在非紧G-凸空间内对具有有限闭值和有限开值的G-KKM,广义G-KKM和广义S-KKM映象建立了某些新的KKM型定理。应用这些KKM型定理,在G-凸空间内得到了新的 Ky Fan型极小极大不等式和鞍点定理。这些结论推广了最近文献中的许多已有结果。