On the Existence of Solutions of Quasi-equilibrium Problems with Constraints

The quasi-equilibrium problems with constraints are formulated and some sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of some vector quasivariational inequality and vector optimization problems. An application of the obtained results is given to show the existence of solutions of quasi-optimization problems with constraints.     

On quasivariational inclusion problems of type I and related problems

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.     

On the Existence of Solutions of Quasivariational Inclusion Problems

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 general vector ideal, proper, Pareto, weak quasioptimization problems, quasivariational inequalities, and vector quasiequilibrium problems. Further, we prove theorems on the existence for solutions of systems of these inclusions. As a corollary, we obtain an ideal minimax theorem concerning vector functions.     

Existences of solutions for generalized vector quasi-equilibrium problems

In the paper, existence theorems for two classes of generalized vector quasi-equilibrium problems are established by using a fixed point theorem and some examples are given to illustrate them. An application to vector quasi-optimization problems is shown. This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 60574073 and 10471142).     

On the existence of solutions to generalized quasi-equilibrium problems

In this paper, we apply new results on variational relation problems obtained by D. T. Luc (J Optim Theory Appl 138:65–76, 2008) to generalized quasi-equilibrium problems. Some sufficient conditions on the existence of its solutions of generalized quasi-equilibrium problems are shown. As special cases, we obtain several results on the existence of solutions of generalized Pareto and weak quasi-equilibrium problems concerning C-pseudomonotone multivalued mappings. We deduce also some results on the existence of solutions to generalized vector Pareto and weakly quasivariational inequality and vector Pareto quasi-optimization problems with multivalued mappings.     

The studies of systems of variational inclusions problems and variational disclusions problems with applications

In this paper, we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems. From these existence results, we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems.     

一类高阶奇异边值问题的正解

本文利用上下解方法给出一类高阶微分方程的奇异边值问题正解的充分条件，改进并推广了韦忠礼在文献［１］中的结果，并指出其证明的漏洞．     

Generalized vector quasi-equilibrium problems with applications to common fixed point theorems and optimization problems

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.     

抽象经济均衡问题解的存在性及其算法

本文首先研究一类新的向量均衡问题,利用截口定理与KKM定理两种不同的工具证明此类均衡问题解的存在性,接着,把这类向量均衡问题推广到更为一般的情形,随后讨论了具有上下界的均衡问题,它是由Isac,Sehgal和Singh于1999年提出的一个公开问题,本文在一定条件下获得了一个新的解的存在性定理,并构造了一个迭代算法,讨论了算法的收敛性。     

Ekeland type variational principle with applications to quasi-variational inclusion problems

In this paper, we study the Ekeland type variational principle, a Caristi-Kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces. By using these results, we establish some existence results for solutions of quasi-variational inclusion problems, quasi-optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces.     

Quasi-Equilibrium Problems and Fixed Point Theorems of Separately l.s.c and u.s.c Mappings

In this paper, we apply our new results on quasi-variational inequality problems to generalized quasi-equilibrium problems. Some su?cient conditions on the existence of solutions are shown. In particular, we establish several results on the existence of solutions to fixed points of separately lower and upper semicontinuous (lower and lower, upper and upper) mappings.These generalize some well-known fixed point theorems obtained by previous authors as Browder and Ky Fan, Wu, et al., etc.     

System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings

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.     

Some existence results for solutions of generalized vector quasi-equilibrium problems

In this paper, we consider more general forms of generalized vector quasi-equilibrium problems for multivalued maps which include many known vector quasi-equilibrium problems and generalized vector quasi-variational inequality problems as special cases. We establish some existence results for solutions of these problems under pseudomonotonicity and u-hemicontinuity/ℓ-hemicontinuity assumptions.      

Generalized vector quasi-equilibrium problems with applications

In this paper, we consider the generalized vector quasi-equilibrium problem with or without involving Φ-condensing maps and prove the existence of its solution by using known fixed point and maximal element theorems. As applications of our results, we derive some existence results for a solution to the vector quasi-optimization problem for nondifferentiable functions and vector quasi-saddle point problem.     

Existence theorems of systems of variational inclusion problems with applications

In this paper, we study the existence theorems of systems of variational inclusions problems. As consequences of our results, we study existence theorems of systems of generalized vector quasi-equilibrium problems, mathematical program with systems of variational inclusion constraints, bilevel problem with systems of constraints.     

Efficiency in vector quasi-equilibrium problems and applications

In this paper, we give sufficient conditions for the existence of efficient solutions of a generalized vector quasi-equilibrium problem in topological vector spaces. The motivations for introducing this problem come from practical problems in traffic networks and the optimal control theory for discrete-time dynamical systems. The main results of the paper are proven with the help of a strongly monotonic function which can be constructed from the data of the problem under consideration. Some notions of cone-semicontinuity of set-valued maps, weaker than the usual concepts of semicontinuity, are also used in our study. As applications, we obtain existence results in vector quasi-optimization problems, Stampacchia set-valued vector quasi-variational inequality problems and Pareto vector quasi-saddle point problems. All these results are different from the corresponding ones in the literature.     

On the generalized vector equilibrium problems

In this paper, generalized vector equilibrium problems are studied and some existence theorems of solutions for these problems in the setting of topological vector spaces are proved. Sufficient conditions for the set of solutions to be compact and convex are given. Our results improve some recent results in this field.     

Variational inclusions problems with applications to Ekeland’s variational principle,fixed point and optimization problems

In this paper, we prove the existence theorems of two types of systems of variational inclusions problem. From these existence results, we establish Ekeland’s variational principle on topological vector space, existence theorems of common fixed point, existence theorems for the semi-infinite problems, mathematical programs with fixed points and equilibrium constraints, and vector mathematical programs with variational inclusions constraints.     

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM, FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS, AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article,we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems,the set of common fixed point for a family of infinite...