Systems of Set-Valued Quasivariational Inclusion Problems

Hải, Nguyễn Xuân; Khánh, Phan Quốc

doi:10.1007/s10957-007-9222-0

Cited by 25 publications

(7 citation statements)

References 26 publications

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“…It is worth noting that the proof presented in Theorem 3.3 is different from the proof given for Theorem 2.1 of [9]. Also it is different to the method presented in [13,25,27,29]. Because they have used a maximal element theorem ( [14,18,30]) for a family of set-valued maps (see, for example, Theorem 2.1 [9]).…”

Section: Remark 33 (A)mentioning

confidence: 99%

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: Remark 33 (A)mentioning

confidence: 99%

On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method

Farajzadeh

Lee

Plubteing

2015

J Optim Theory Appl

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“…The set-valued mappings S, T, and F are said to be a constraint, a potential, and a utility mapping, respectively. These problems play a central role in vector optimization theory concerning set-valued mappings and have close relations with vector quasi-equilibrium problems, vector quasi-variational inequality problems, fixed point problems, quasi saddle problems, and minimax problems, for example, see [1][2][3][4][5][6][7][8] and the references therein. Lin and Tan [1] proved some existence results of solutions for these above problems under suitable assumptions.…”

Section: Introductionmentioning

confidence: 99%

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

Ding

2009

Appl. Math. Mech.-Engl. Ed.

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In this paper, we introduce some new systems of generalized vector quasivariational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally F C-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems. Key wordsKKM type theorem, Himmelberg type fixed point theorem, system of generalized vector quasi-variational inclusions, system of generalized vector optimization problems, locally F C-uniform space Chinese Library Classification O176.3, O177.92 2000 Mathematics Subject Classification 49J27, 49J53, 91B50, 90C48 *

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“…Recently, using different methods, several authors further considered inclusion and disclusion problems for multi-valued mappings such as systems of inclusion problems, variational and quasivariational inclusion problems, variational disclusion problems, vector quasivariational inclusion problems and their applications; see, for example, [15,22,25,26,29] and the references therein.…”

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confidence: 99%

Generalized Implicit Inclusion Problems on Noncompact Sets With Applications

Wang

Huang²

2011

Bull. Aust. Math. Soc.

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In this paper, a class of generalized implicit inclusion problems is introduced, which can be regarded as a generalization of variational inequality problems, equilibrium problems, optimization problems and inclusion problems. Some existence results of solutions for such problems are obtained on noncompact subsets of Hausdorff topological vector spaces using the famous FKKM theorem. As applications, some existence results for vector equilibrium problems and vector variational inequalities on noncompact sets of Hausdorff topological vector spaces are given.2010 Mathematics subject classification: primary 49J40.

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Systems of Set-Valued Quasivariational Inclusion Problems

Cited by 25 publications

References 26 publications

On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method

On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

Generalized Implicit Inclusion Problems on Noncompact Sets With Applications

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