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1.
In this paper, we introduce several kinds of maximal pseudomonotonicity and establish existence theorems of maximal pseudomonotonicity.
From these results we establish the existence theorems of generalized vector equilibrium problems. We establish existence
theorems of generalized vector semi-infinite programming, as applications of generalized vector equilibrium problems.
This research was supported by the National Science Council of the Republic of China. 相似文献
2.
In this paper, we establish some equivalence relations between coincidence theorems and KKM-type theorems. We also obtain some new coincidence theorems and fixed point theorems. Applying the KKM-type theorems we obtain the existence theorems of generalized vector equilibrium problems. From these results, some existence theorems of generalized vector implicit variational inequality problems are established in this paper. 相似文献
3.
Zhi Lin 《Journal of Global Optimization》2006,36(4):627-635
In this paper, we study the system of generalized vector quasi-equilibrium problems, which includes as special cases the system of vector quasi-equilibrium problems and the system of generalized vector equilibrium problems, and establish the existence and essential components of the solution set under perturbations of its best-reply map. Moreover, we also derive a new existence theorem of Ky Fan’s points for a set-valued map. 相似文献
4.
Xie Ping Ding 《Journal of Global Optimization》2007,38(3):367-385
This paper is a continuum of the preceding paper of author. By applying a coincidence theorem in noncompact FC-space without
any convexity structure due to author, a new KKM type theorem is first proved under noncompact setting of FC-spaces. The equivalent
relation between the coincidence theorem and the KKM type theorem is also established. As applications of the KKM type theorem,
we establish some new existence theorems of solutions for three classes of generalized vector equilibrium problems under noncompact
setting of FC-spaces. These theorems improve and generalize many known results in literature. 相似文献
5.
The purpose of this paper is to study systems of vector equilibrium problems. We establish some existence theorems for systems
of vector equilibrium problems by using (S)+-conditions and Kakutani–Fan–Glicksberg fixed point theorem
*This work was supported by the Kyungnam University Research Fund 2004 相似文献
6.
Lai-jiu Lin 《Journal of Global Optimization》2006,34(1):15-32
In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence
theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also
obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of
the Debreu vector equilibrium problems and the Nash vector equilibrium problems. 相似文献
7.
In this paper, we first establish some existence theorems of systems of generalized vector equilibrium problems. From these
results, we obtain new variants of Ekeland’s variational principle in a Hausdorff t.v.s., a minimax theorem and minimization
theorems. Some applications to the existence theorem of systems of semi-infinite problem, a variant of flower petal theorem
and a generalization of Schauder’s fixed point theorem are also given. 相似文献
8.
In this paper, we consider a class of operator equilibrium problems (OEP for short) with operator solutions and derive a Minty type lemma for this class of problems. Further, using this lemma and KKM theorem, we establish some existence theorems for OEP. The theorems presented in this paper generalize, improve and unify many known results. 相似文献
9.
Z. Lin 《Journal of Optimization Theory and Applications》2005,124(2):387-405
In this paper, we study the existence and essential components of the set of weakly Pareto-Nash equilibrium points for multiobjective generalized games in two different uniform topological spaces. We obtain some new existence theorems. Examples show that the results are not identical in two different topological spaces.The author thanks two referees for careful reading of the paper and helpful comments. 相似文献
10.
The quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown.
As special cases, we obtain several results on the existence of solutions of a general vector ideal (proper, Pareto, weak)
quasi-optimization problems, of quasivariational inequalities, and of vector quasi-equilibrium problems. Further, we prove
theorems on the existence for solutions of the sum of these inclusions. As corollaries, we shall show several results on the
existence of solutions to another problems in the vector optimization problems concerning multivalued mappings.
This work was supported by the National Science Council of the Republic of China and the Academy of Sciences and Technologies
of Vietnam.
The authors wish to express their gratitude to the referees for their valuable suggestions. 相似文献
11.
In this paper, we first establish the existence theorems of generalized vector quasi-equilibrium problems. From these results, we establish the existence theorems of common fixed point theorems for two multivalued maps and mathematical programs with an equilibrium constraint as applications. 相似文献
12.
13.
A new KKM type theorem is first proved under noncompact setting of FC-spaces. As applications of the KKM type theorem, we establish some new existence theorems of solutions for generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature. 相似文献
14.
Xie-Ping Ding Jen-Chih Yao Lai-Jiu Lin 《Journal of Mathematical Analysis and Applications》2004,298(2):398-410
In this paper we establish a collectively fixed point theorem and an equilibrium existence theorem for generalized games in product locally G-convex uniform spaces. As applications, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are derived in product locally G-convex uniform spaces. These theorems are new and generalize some known results in the literature. 相似文献
15.
Qun Luo 《Journal of Global Optimization》2006,34(4):589-595
In the paper, by using Ky Fan’s section theorem, we obtain an existence theorem for vector equilibrium problems. Motivated
by the ideas of Kinoshita and McLennan, we introduce the concept of the essential component of the solution set for vector
equilibrium problems, and we prove that there exists at least one essential component of the solution set for every vector
equilibrium problem satisfying some conditions.
Research was partially supported by the Natural Science Foundation of Guangdong Province, P. R. China. 相似文献
16.
Xie Ping DING 《数学学报(英文版)》2007,23(10):1869-1880
In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature. 相似文献
17.
In this paper, we establish existence theorems of quasivariational inclusion problems; from them, we establish existence theorems
of mathematical programs with quasivariational inclusion constraint, bilevel problems, mathematical programs with equilibrium
constraint and semi-infinite problems.
This research was supported by the National Science Council of the Republic of China. The authors express their gradtitude
to the referees for valuable suggestions. 相似文献
18.
In this paper, we apply a new version of the Brézis, Nirenberg, and Stampacchia theorem; we use pseudomonotonicity and some coercivity conditions to establish some existence result for a solution of generalized vector equilibrium problems for multivalued bifunctions. The proper quasiconvexity of multivalued bifunctions is introduced and existence theorems for generalized vector equilibrium problems related to multivalued mappings with the KKM property are obtained. The new results extend and modify various existence theorems for similar problems. 相似文献
19.
In this paper, we use existence theorems for the equilibria of generalized abstract economies proved recently to establish existence theorems for systems of generalized vector quasiequilibrium problems. Then, these existence theorems for equilibrium problems are used to derive existence theorems for systems of generalized vector quasivariational-like inequality problems, and vector quasioptimization problems.This research was supported by the National Science Council of the Republic of China. The authors express their gratitude to the referees for valuable suggestions. 相似文献
20.
In this paper, we introduce systems of simultaneous generalized vector equilibrium problems and prove the existence of their
solutions. As application of our results, we derive the existence theorems for solutions of systems of vector saddle–point
problems. Consequently, we prove the existence of a solution of systems of generalized minimax inequalities. Further application
of our results is also given to establish the existence of a solution of a Debreu-type equilibrium problem for vector-valued
functions.
The first author thanks the Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran,
Saudi Arabia for providing excellent research facilities. The second and third authors were supported by the National Science
Council of the Republic of China. The authors are grateful to the referees for valuable suggestions and comments. 相似文献