Nguyen Xuan Hai

Nguyen Xuan Hai
Posts and Telecommunications Institute of Technology | PTIT · Department of Scientific Fundamentals 2

PhD

About

9
Publications
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282
Citations

Publications

Publications (9)
Article
In this paper, we first introduce systems of quasi-variational inclusion problems on Hadamard manifolds and establish the existence conditions of the solution set of these systems using the Kakutani-Fan-Glicksberg fixed-point theorem. Then, we study essential components of the solution to such problems. Finally, as applications, we consider the spe...
Article
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In this paper we consider stochastic equilibrium problems involving parameter of probability measures. Employing KKM-Fan xed point theorem, conditions for the existence of solutions to such problems are established. We then propose new metric concepts on the underlying stochastic spaces and study some properties corresponding to these metrics. Afte...
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We establish sufficient existence conditions for general quasivaria- tional inclusion problems, which contain most of variational inclusion problems and quasiequilibrium problems considered in the literature. These conditions are shown to extend recent existing results and sharpen even results for particular cases.
Article
We establish a maximal element theorem, an intersection theorem and a coincidence-point theorem in product GFC-spaces. As examples of wide ranges of applications, we first deduce sufficient conditions for the solution existence of a mixed system of inclusions. Then using this we obtain existence results for systems of vector quasi-optimization prob...
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We propose four kinds of systems of set-valued quasivariational inclusion problems in product spaces, which include many known systems of equilibrium problems and systems of variational inequalities as well as inclusion problems. Sufficient conditions for the solution existence are established. When applied to special cases, these conditions improv...
Article
We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclus...
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A general quasiequilibrium problem is proposed including, among others, equilibrium problems, implicit variational inequalities, and quasivariational inequalities involving multifunctions. Sufficient conditions for the existence of solutions with and without relaxed pseudomonotonicity are established. Even semicontinuity may not be imposed. These c...
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We consider three types of approximate solutions of multivalued quasiequilibrium vector problems. Sucient conditions for the "-solution existence are established for variants of such problems. Several applications are provided as examples to show that our results can imply consequences about approximate solutions of many optimization-related proble...
Article
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We propose a general problem setting for systems of multivalued vector quasiequi-librium problems in topological vector spaces to include recent introduced models. Sufficient conditions for the solution existence are established and shown to improve existing results or to be new even for paticular cases. Applications in fixed point and coincidence...

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