The Systems for Generalized of Vector Quasiequilibrium Problems and Its Applications
Main Article Content
Abstract
Abstract: In this paper, we study the systems of generalized quasiequilibrium problems which includes as special cases the generalized vector quasi-equilibrium problems, vector quasiequilibrium problems, and establish the existence results for its solutions by using fixed-point theorem. Moreover, we also discuss the closedness of the solution sets of systems of generalized quasiequilibrium problems. As special cases, we also derive the existence results for vector quasiequilibrium problems and vector quasivariational inequality problems. Our results are new and improve recent existing ones in the literature.
Keywords: Systems of generalized quasiequilibrium problems, quasiequilibrium problems, quasivariational inequality problem, fixed-point theorem, existence, closedness.References
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[13] J.P. Aubin and I. Ekeland (1984), Applied Nonlinear Analysis, John Wiley and Sons, New York.
[14] E. Blum and W. Oettli (1994), From optimization and variational inequalities to equilibrium problems, Math. Student, 63, pp 123-145.
[2] Q.H. Ansari, S. Schaible and J.C. Yao (2002), System of generalized vector equilibrium problems with applications J. Global Optim, 22, pp 3-16.
[3] Q.H. Ansari (2008), Existence of solutions of systems of generalized implicit vector quasi-equilibrium problems, J. Math. Anal. Appl, 341, pp 1271-1283.
[4] S. Plubtieng and K. Sitthithakerngkiet(2011), On the existence result for system of generalized strong vector quasi-equilibrium problems. Fixed Point Theory and Applications. Article ID 475121, doi:10.1155/2011/475121
[5] Y. Yang and Y.J. Pu(2013), On the existence and essential components for solution set for symtem of strong vector quasiequilibrium problems. J. Global Optim. 55, pp 253-259.
[6] N. V. Hung and P. T. Kieu(2013), Stability of the solution sets of parametric generalized quasiequilibrium problems, VNU- Journal of Mathematics – Physics, 29, pp 44-52,
[7] K. Fan (1961), A generalization of Tychonoff’s fixed point theorem. Math Ann. 142, pp 305--310.
[8] X.J. Long, N.J. Huang, K.L.Teo(2008), Existence and stability of solutions for generalized strong vector quasi-equilibrium problems. Mathematical and Computer Modelling. 47, pp 445-451
[9] E. Blum and W. Oettli (1994), From optimization and variational inequalities to equilibrium problems, Math. Student, 63, pp 123-145.
[10] N. V. Hung (2013), Existence conditions for symmetric generalized quasi-variational inclusion problems, Journal of Inequalities and Applications, 40, pp 1-12.
[11] J. Yu (1992), Essential weak efficient solution in multiobjective optimization problems. J. Math. Anal. Appl. 166, pp 230-235.
[12] G. Y. Chen, X.X. Huang and X. Q. Yang (2005), Vector Optimization: Set-Valued and Variational Analysis, Lecture Notes in Economics and Mathematical Systems, 541, Springer, Berlin.
[13] J.P. Aubin and I. Ekeland (1984), Applied Nonlinear Analysis, John Wiley and Sons, New York.
[14] E. Blum and W. Oettli (1994), From optimization and variational inequalities to equilibrium problems, Math. Student, 63, pp 123-145.