Existence conditions for symmetric generalized quasi-variational inclusion problems

Ansari QH, Oettli W, Schiager D: A generalization of vectorial equilibria. Math. Methods Oper. Res. 1997, 46: 147–152. 10.1007/BF01217687 Ansari QH, Schaible S, Yao JC: System of generalized vector equilibrium problems with applications. J. Glob. Optim. 2002, 22: 3–16. 10.1023/A:1013857924393 Ansari QH, Konnov IV, Yao JC: On generalized vector equilibrium problems. Nonlinear Anal. TMA 2001, 47: 543–554. 10.1016/S0362-546X(01)00199-7 Long XJ, Huang NJ, Teo KL: Existence and stability of solutions for generalized strong vector quasi-equilibrium problems. Math. Comput. Model. 2008, 47: 445–451. 10.1016/j.mcm.2007.04.013 Plubtieng S, Sitthithakerngkiet K: On the existence result for system of generalized strong vector quasi-equilibrium problems. Fixed Point Theory Appl. 2011., 2011: Article ID 475121 Chen B, Huang NJ, Cho YJ: Symmetric strong vector quasiequilibrium problems in Hausdorff locally convex spaces. J. Inequal. Appl. 2011., 2011: Article ID 56 Hung NV: Sensitivity analysis for generalized quasi-variational relation problems in locally G -convex spaces. Fixed Point Theory Appl. 2012., 2012: Article ID 158 Hung NV: Continuity of solutions for parametric generalized quasi-variational relation problems. Fixed Point Theory Appl. 2012., 2012: Article ID 102 Anh LQ, Khanh PQ: On the stability of the solution sets of general multivalued vector quasiequilibrium problems. J. Optim. Theory Appl. 2007, 135: 271–284. 10.1007/s10957-007-9250-9 Anh LQ, Khanh PQ: Existence conditions in symmetric multivalued vector quasiequilibrium problem. Control Cybern. 2008, 36: 519–530. Fu JY: Symmetric vector quasiequilibrium problems. J. Math. Anal. Appl. 2003, 285: 708–713. 10.1016/S0022-247X(03)00479-7 Lin LJ, Liu YH: Existence theorems for systems of generalized vector quasiequilibrium problems and optimization problems. J. Optim. Theory Appl. 2006, 130: 461–475. Kien BT, Huy NQ, Wong NC: On the solution existence of generalized vector quasi-equilibrium problems with discontinuous multifunctions. Taiwan. J. Math. 2009, 13: 757–775. Liu QY, Long XJ, Huang NJ: Connectedness of the sets of weak efficient solutions for generalized vector equilibrium problems. Math. Slovaca 2012, 62: 123–136. 10.2478/s12175-011-0077-3 Long XJ, Peng JW: Connectedness and compactness of weak efficient solutions for vector equilibrium problems. Bull. Korean Math. Soc. 2011, 48: 1225–1233. Long XJ, Huang YQ, Peng ZY: Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints. Optim. Lett. 2011, 5: 717–728. 10.1007/s11590-010-0241-7 Lin Z, Yang H, Yu J: On existence and essential components of the solution set for the system of vector quasiequilibrium problems. Nonlinear Anal. 2005, 63: 2445–2452. 10.1016/j.na.2005.03.049 Lin Z, Yu J: The existence of solutions for the system of generalized vector quasiequilibrium problems. Appl. Math. Lett. 2005, 18: 415–422. 10.1016/j.aml.2004.07.023 Song QQ, Wang LS: The existence of solutions for the system of vector quasiequilibrium problems in topological order spaces. Comput. Math. Appl. 2011, 62: 1979–1983. 10.1016/j.camwa.2011.06.041 Plubtieng S, Sitthithakerngkiet K: Existence result of generalized vector quasiequilibrium problems in locally G -convex spaces. Fixed Point Theory Appl. 2011., 2011: Article ID 967515 Yang Y, Pu YJ: On the existence and essential components for solution set for system of strong vector quasiequilibrium problems. J. Glob. Optim. 2011. doi:10.1007/s10898–011–9830-y Blum E, Oettli W: From optimization and variational inequalities to equilibrium problems. Math. Stud. 1994, 63: 123–145. Hou SH, Gong XH, Yang XM: Existence and stability of solutions for generalized Ky Fan inequality problems with trifunctions. J. Optim. Theory Appl. 2010, 146: 387–398. 10.1007/s10957-010-9656-7 Lin Z: Existence of solutions to the system of generalized implicit vector quasivariational inequality problems. Fixed Point Theory Appl. 2009., 2009: Article ID 654370 Balaj M, Lin LJ: Generalized variational relation problems with applications. J. Optim. Theory Appl. 2011, 148: 1–13. 10.1007/s10957-010-9741-y Yu J: Essential weak efficient solution in multiobjective optimization problems. J. Math. Anal. Appl. 1992, 166: 230–235. 10.1016/0022-247X(92)90338-E Berge C: Topological Spaces. Oliver and Boyd, London; 1963. Luc DT: Theory of Vector Optimization: Lecture Notes in Economics and Mathematical Systems. Springer, Berlin; 1989. Holmes RB: Geometric Functional Analysis and Its Application. Springer, New York; 1975.