On the Solution Existence of Generalized Vector Quasi-Equilibrium Problems With Discontinuous Multifunctions

Kien, B. T.; Huy, Nguyễn Quang; Wong, Ngai–Ching

doi:10.11650/twjm/1500405401

Cited by 3 publications

(3 citation statements)

References 27 publications

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“…Finally, we introduce a general form of Nash equilibrium problem and apply our results in order to establish some existence theorems for it. The results presented in this paper generalized some corresponding results in the literature (for instance [9][10][11] and [12] for single-valued maps).…”

Section: Introductionsupporting

confidence: 83%

“…(b) By comparing Theorem 3.1 with Theorem 3.2 of [11], one can understand that the previous theorem is an infinite dimensional version of Theorem 3.2 [11] with mild assumptions.…”

Section: Remark 31 (A) Theorem 31 Improves Theorem 32 Ofmentioning

confidence: 98%

“…(c) If we define Q i (y) = K i , V i (x) = K i , and C(x) = P (P is a fixed closed and convex cone with nonempty interior) for all i ∈ I , y ∈ K i and x ∈ Y = i∈I K i , then (SGVQEP) reduces to the system of vector equilibrium problem (SVEP) introduced and studied in [9], and also it is a general form of the problem introduced in [11] for a moving cone. Moreover, one can consider (SGVQEP) as another version of generalized abstract economy problem considered in [12] and as a system of generalized quasivector equilibrium problems for a moving cone and for single-valued maps studied in [13].…”

Section: Remark 33 (A)mentioning

confidence: 99%

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On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method

Farajzadeh

Lee

Plubteing

2015

J Optim Theory Appl

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In this paper, we consider the nonlinear scalarization function in the setting of topological vector spaces and present some properties of it. Moreover, using the nonlinear scalarization function and Fan-Glicksberg-Kakutani's fixed point theorem, we obtain an existence result of a solution for a generalized vector quasi-equilibrium problem without using any monotonicity and upper semi-continuity (or continuity) on the given maps. Our result can be considered as an improvement of the known corresponding result. After that, we introduce a system of generalized vector quasiequilibrium problem which contains Nash equilibrium and Debreu-type equilibrium problem as well as the system of vector equilibrium problem posed previously. We provide two existence theorems for a solution of a system of generalized vector quasiequilibrium problem. In the first one, our multi-valued maps have closed graphs and the maps are continuous, while in the second one, we do not use any continuity on the maps. Moreover, the method used for the existence theorem of a solution of a system of generalized vector quasi-equilibrium problem is not based upon a maximal element theorem. Finally, as an application, we apply the main results to study a system of vector optimization problem and vector variational inequality problem.

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Section: Introductionsupporting

confidence: 83%

“…(b) By comparing Theorem 3.1 with Theorem 3.2 of [11], one can understand that the previous theorem is an infinite dimensional version of Theorem 3.2 [11] with mild assumptions.…”

Section: Remark 31 (A) Theorem 31 Improves Theorem 32 Ofmentioning

confidence: 98%

Section: Remark 33 (A)mentioning

confidence: 99%

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On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method

Farajzadeh

Lee

Plubteing

2015

J Optim Theory Appl

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Existence conditions for symmetric generalized quasi-variational inclusion problems

Hùng

2013

J Inequal Appl

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In this paper, we establish an existence theorem by using the Kakutani-Fan-Glicksberg fixed-point theorem for a symmetric generalized quasi-variational inclusion problem in real locally convex Hausdorff topological vector spaces. Moreover, the closedness of the solution set for this problem is obtained. As special cases, we also derive the existence results for symmetric weak and strong quasi-equilibrium problems. The results presented in the paper improve and extend the main results in the literature. MSC: 90B20; 49J40

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Sensitivity analysis for generalized quasi-variational relation problems in locally G-convex spaces

Hùng

2012

Fixed Point Theory Appl

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In this paper, we study generalized quasi-variational relation problems in locally G-convex spaces. Using the Kakutani-Fan-Glicksberg fixed-point theorem for upper semicontinuous set-valued mapping with nonempty closed acyclic values, we establish an existence theorem of a solution set for these problems. Moreover, the stability and closedness of the solution set for these problems are also obtained. The results presented in the paper improve and extend the main results in the literature. MSC: 47J20; 49J40

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On the Solution Existence of Generalized Vector Quasi-Equilibrium Problems With Discontinuous Multifunctions

Cited by 3 publications

References 27 publications

On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method

On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method

Existence conditions for symmetric generalized quasi-variational inclusion problems

Sensitivity analysis for generalized quasi-variational relation problems in locally G-convex spaces

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