Abstract
In this paper, we study the system of strong vector quasi-equilibrium problems without assuming that the dual of the ordering cone has a weak* compact base. We show the existence and essential components of solution set for system of strong vector quasi-equilibrium problems by defining the best-reply mapping.
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Ansari Q.H., Schaible S., Yao J.C.: The system of generalized vector equilibrium problems with applications. J. Global Optim. 22, 3–16 (2002)
Hillas J.: On the definition of the strategic stability of equilibria. Econometrica 58, 1365–1390 (1990)
Jameson, G.: Order Linear Spaces. In: Lector Notes in Math, vol. 141. Springer, Berlin (1970)
Gong X.H.: Efficiency and Henig efficiency for vector equilibrium problem. J. Optim. Theory Appl. 108, 139–154 (2001)
Gong X.H.: Strong vector equilibrium problem. J. Global Optim. 36, 339–349 (2006)
Hou, S.H., Gong, X.H., Yang, X.M.: Existence and stability of solutions for generalized strong vector equilibrium problems with trifunctions. J. Optim. Theory Appl. (in press)
Jiang J.H.: Essential component of the set of fixed points of the multivalued mappings and its application to the theory of games. Sci. Sin. 12, 951–964 (1963)
Kohlberg E., Mertens J.F.: On the strategic stability of equilibria. Econometrica 54, 1003–1037 (1986)
Yang H., Yu J.: On essential components of the set of weakly Pareto–Nash equilibrium points. Appl. Math. Lett. 15, 553–560 (2002)
Yu J., Luo Q.: On essential components of the solution set of generalized games. J. Math. Anal. Appl. 230, 303–310 (1999)
Yu J., Xiang S.W.: On essential components of the set of Nash equilibrium points. Nonlinear Anal. Theory Methods Appl. 38, 259–264 (1999)
Deguire P., Tan K.-K., Yuan X.-Z.: The study of maximal elements, fixed points for L s -majorized mapping and their applications to minimax and variational inequalities in the product topological spaces. Nonlinear Anal. Theory Methods Appl. 37, 933–951 (1999)
Fan K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequalities III, pp. 103–113. Academic Press, New York (1972)
Wu X., Shen S.K.: A further generalization of Yannelis–Prabhakars continuous selection theorem and its applications. J. Math. Anal. Appl. 197, 61–74 (1996)
Wu X., Yuan X.-Z.: On equilibrium problem of abstract economy, generalized quasi-variational inequality, and an optimization problem in locally H-convex spaces. J. Math. Anal. Appl 282, 495–505 (2003)
Yu H.: Weak Pareto equilibria for multiobjective constrained games. Appl. Math. Lett. 16, 773–776 (2003)
Yu J., Yuan G.X.-Z.: The study of Pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods. Comput. Math. Appl 35, 17–24 (1998)
Pardalos P.M., Rassias T.M., Khan A.A.: Nonlinear Analysis and Variational Problems. Springer, Berlin (2010)
Li X.B., Li S.J.: Existence of solutions for generalized vector quasi-equilibrium problems. Optim. Lett. 4(1), 17–28 (2010)
Lin L.J.: System of generalized vector quasi-equilibrium problems with applications to fixed point theorems for a family of nonexpansive multivalued mappings. J. Global Optim. 34(1), 15–32 (2006)
Giannessi F., Maugeri A., Pardalos P.M.: Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. Kluwer Academic Publishers, Dordrecht (2002)
Panagiotopoulos P.D., Pardalos P.M.: From Convexity to Nonconvexity. co-editors: R.P. Kluwer Academic Publishers, Dordrecht (2001)
Aubin J.P., Ekeland I.: Applied Nonlinear Analysis. Wiley, New York (1984)
Deguire P., Tan K.-K., Yuan X.-Z.: The study of maximal elements, fixed points for L s -majorized mapping and their applications to minimax and variational inequalities in the product topological spaces. Nonlinear Anal. Theory Methods Appl. 37, 933–951 (1999)
Fan K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequalities III, pp. 103–113. Academic Press, New York (1972)
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Yang, Z., Pu, Y.J. On existence and essential components for solution set for system of strong vector quasi-equilibrium problems. J Glob Optim 55, 253–259 (2013). https://doi.org/10.1007/s10898-011-9830-y
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DOI: https://doi.org/10.1007/s10898-011-9830-y