Generalized Vector Equilibrium Problems Research Articles

On Generalized Vector Equilibrium Problems

A new generalized vector equilibrium problem involving set-valued mappings and the proper quasi-concavity of set-valued mappings in topological vector spaces are introduced; its existence theorems and the convexity of the solution sets are established.

Existence Results for Primal and Dual Generalized Vector Equilibrium Problems With Applications to Generalized Semi-Infinite Programming

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.

Systems of Simultaneous Generalized Vector Quasiequilibrium Problems and their Applications

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.

Recession methods for generalized vector equilibrium problems

By using the recession method, we give some necessary and/or sufficient condition of solutions of generalized vector equilibrium problems.

Generalized Vector Equilibrium Problems for Pseudomonotone Multivalued Bifunctions1

In this paper, we apply a new version of the Brezis, 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.

Generalized vector quasi-equilibrium problems in locally G-convex spaces

Some classes of generalized vector quasi-equilibrium problems (in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems, generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.

The Study of KKM Theorems With Applications to Vector Equilibrium Problems and Implict Vector Variational Inequalities Problems

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.

The existence of solutions for the system of generalized vector quasi-equilibrium problems

In this paper, we study the system of generalized vector quasi-equilibrium problems which includes as special cases the system of generalized vector equilibrium problems and the system of vector quasi-equilibrium problems, and establish the existence result for its solutions by means of the Kakutani–Fan–Glicksberg fixed points theorem. As special cases, we also derive the existence results for weakly Pareto–Nash equilibrium points for multiobjective generalized game problems and multiobjective game problems.

Generalized Vector Equilibrium Problems with Trifunctions

In this paper, we study the existence of strong and weak solutions of the generalized vector equilibrium problems for trifunctions. Two special classes of vector-valued trifunctions are introdcued, called the classes of (SPM) and (GPM), respectively. Some existence results for strong solutions associated to functions of these classes are given.

KKM Type Theorems and Coincidence Theorems with Applications to the Existence of Equilibria

In this paper, we obtain some coincidence theorems and some KKM-type theorems. We apply these results to establish the existence of the solution to generalized vector equilibrium problems, where a bimap f : X × Y → 2Z is involved and some sufficient conditions are imposed on f.

Nonempty intersection theorems and system of generalized vector equilibrium problems in product G-convex spaces

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

Generalized Vector Equilibrium Problems in Generalized Convex Spaces

In this paper, we introduce and study a class of abstract generalized vector equilibrium problems (AGVEP) in generalized convex spaces which includes most vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems, and generalized vector variational inequality problems as special cases. By using the generalized GKKM and generalized SKKM type theorems due to the first author, some new existence results of equilibrium points for the AGVEP are established in noncompact generalized convex spaces. As consequences, some recent results in the literature are obtained under much weaker assumptions.

Geometric Properties and Coincidence Theorems with Applications to Generalized Vector Equilibrium Problems

The present paper is divided into two parts. In the first part, we derive a Fan-KKM type theorem and establish some Fan type geometric properties of convex spaces. By applying our results, we also obtain some coincidence theorems and fixed-point theorems in the setting of convex spaces. The second part deals with the applications of our coincidence theorem to establish some existence results for a solution to the generalized vector equilibrium problems.

Generalized vector equilibrium problems with set-valued mappings

In this paper, we introduce a more general form of vector equilibrium problems with a moving ordering cone and set-valued mappings, and obtain some existence theorems for generalized vector equilibrium problems, which extend and unify some existence results for similar problems.

On generalized vector equilibrium problems

An existence result for a generalized vector equilibrium problem is proved in a general topological vector space. As applications, existence results are derived for vector equilibrium problems and vector variational-like inequalities with set-valued mappings under Ψ -monotonicity condition and maximal Ψ -monotonicity condition. These results extend and unify a number of existence results for vector variational inequalities in the previous literature.

Generalized vector equilibrium problems

In this paper we survey results concerning the existence of a solution to the generalized vector equilibrium problem which includes implicit vector variational inequality problems, extended generalized vector variational-like inequality problems, vector variational inequality problems and vector equilibrium problems as special cases. The analysis is done for both Cx -pseudomonotone and Cx -quasimonotone multifunctions and also without these monotonícities.

The system of generalized vector equilibrium problems with applications

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.

On generalized vector equilibrium problems

On generalized vector equilibrium problems

Existence and Duality of Generalized Vector Equilibrium Problems

In this paper, we propose some dual formulations of generalized vector equilibrium problems. By using such dual formulations, we prove the existence of a solution to the generalized vector equilibrium problem under generalized pseudomonotonicity conditions. The results of this paper extend and generalize the results of I.V. Konnov and S. Schaible (2000, J. Optim. Theory Appl., 104, 395–408).

Topological KKM theorems and generalized vector equilibria on G-convex spaces with applications

In the present paper, slightly modifying the topological KKM Theorem of Park and Kim (1996), we obtain a new existence theorem for generalized vector equilibrium problems related to an admissible multifunction. We work here under the general framework of G-convex space which does not have any linear structure. Also, we give applications to greatest element, fixed point and vector saddle point problems. The results presented in this paper extend and unify many results in the literature by relaxing the compactness, the closedness and the convexity conditions.