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Various kinds of semicontinuity and the solution sets of parametric multivalued symmetric vector quasiequilibrium problems. (English) Zbl 1165.90026

The authors study various quasi-equilibrium problems involving set-valued maps in infinite dimensional spaces. They introduce some new kinds of continuity for set-valued maps and establish these properties for the solution sets, in particular Hausdorff upper and lower semicontinuity and continuity with respect to a partially ordering cone are also addressed.

MSC:

90C31 Sensitivity, stability, parametric optimization
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[1] Ait Mansour, M., Riahi, H.: Sensitivity analysis for abstract equilibrium problems. J. Math. Anal. Appl. 306, 684–691 (2005) · Zbl 1068.49005 · doi:10.1016/j.jmaa.2004.10.011
[2] Anh, L.Q., Khanh, P.Q.: Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems. J. Math. Anal. Appl. 294, 699–711 (2004) · Zbl 1048.49004 · doi:10.1016/j.jmaa.2004.03.014
[3] Anh, L.Q., Khanh, P.Q.: On the Hölder continuity of solutions to parametric multivalued vector equilibrium problems. J. Math. Anal. Appl. 321, 308–315 (2006) · Zbl 1104.90041 · doi:10.1016/j.jmaa.2005.08.018
[4] Anh, L.Q., Khanh, P.Q.: On the stability of the solution sets of general multivalued vector quasiequilibrium problems. J. Optim. Theory Appl. 135, 271–284 (2007a) · Zbl 1146.90516 · doi:10.1007/s10957-007-9250-9
[5] Anh, L.Q., Khanh, P.Q.: Uniqueness and Hölder continuity of the solution to multivalued equilibrium problems in metric spaces. J. Glob. Optim. 37, 449–465 (2007b) · Zbl 1156.90025 · doi:10.1007/s10898-006-9062-8
[6] Anh, L.Q., Khanh, P.Q.: Existence conditions in symmetric multivalued vector quasiequilibrium problems. Control Cyber. 36, 519–530 (2007c) · Zbl 1166.49017
[7] Anh, L.Q., Khanh, P.Q.: Semicontinuity of the approximate solution sets of multivalued quasiequilibrium problems. (2007c) · Zbl 1211.90243
[8] Ansari, Q.H., Schaible, S., Yao, J.C.: The system of vector equilibrium problems and its applications. J. Optim. Theory Appl. 107, 547–557 (2000) · Zbl 0972.49009 · doi:10.1023/A:1026495115191
[9] Ansari, Q.H., Schaible, S., Yao, J.C.: The system of generalized vector equilibrium problems with applications. J. Glob. Optim. 22, 3–16 (2002) · Zbl 1041.90069 · doi:10.1023/A:1013857924393
[10] Bianchi, M., Pini, R.: A note on stability for parametric equilibrium problems. Oper. Res. Lett. 31, 445–450 (2003) · Zbl 1112.90082 · doi:10.1016/S0167-6377(03)00051-8
[11] Bianchi, M., Pini, R.: Sensitivity for parametric vector equilibria. Optimization 55, 221–230 (2006) · Zbl 1149.90156 · doi:10.1080/02331930600662732
[12] Bianchi, M., Schaible, S.: Equilibrium problems under generalized convexity and generalized monotonicity. J. Glob. Optim. 30, 121–134 (2004) · Zbl 1066.90080 · doi:10.1007/s10898-004-8269-9
[13] Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123–145 (1994) · Zbl 0888.49007
[14] Farajzadeh, A.P.: On the symmetric vector quasiequilibrium problems. J. Math. Anal. Appl. 322, 1099–1110 (2006) · Zbl 1130.49008 · doi:10.1016/j.jmaa.2005.09.079
[15] Fu, J.Y.: Symmetric vector quasiequilibrium problems. J. Math. Anal. Appl. 285, 708–713 (2003) · Zbl 1031.49013 · doi:10.1016/S0022-247X(03)00479-7
[16] Hai, N.X., Khanh, P.Q.: Existence of solutions to general quasiequilibrium problems and applications. J. Optim. Theory Appl. 133, 317–327 (2007a) · Zbl 1146.49004 · doi:10.1007/s10957-007-9170-8
[17] Hai, N.X., Khanh, P.Q.: The solution existence of general variational inclusion problems. J. Math. Anal. Appl. 328, 1268–1277 (2007b) · Zbl 1108.49020 · doi:10.1016/j.jmaa.2006.06.058
[18] Hai, N.X., Khanh, P.Q.: Systems of set-valued quasivariational inclusion problems. J. Optim. Theory Appl. 135, 55–67 (2007c) · Zbl 1126.49022 · doi:10.1007/s10957-007-9222-0
[19] Hai, N.X., Khanh, P.Q.: Systems of multivalued quasiequilibrium problems. Adv. Nonlinear Var. Inequal. 9, 97–108 (2006) · Zbl 1181.49009
[20] Haung, N.J., Li, J., Thompson, H.B.: Stability for parametric implicit vector equilibrium problems. Math. Comput. Model. 43, 1267–1274 (2006) · Zbl 1187.90286 · doi:10.1016/j.mcm.2005.06.010
[21] Hu, S., Papageorgiou, N.S.: Handbook of Multivalued Analysis. Kluwer, London (1997) · Zbl 0887.47001
[22] Iusem, A.N., Sosa, W.: New existence results for equilibrium problems. Nonlinear Anal. 52, 621–635 (2003) · Zbl 1017.49008 · doi:10.1016/S0362-546X(02)00154-2
[23] Lin, L.J.: Systems of generalized vector quasiequilibrium problems with applications to fixed point theorems for a family of nonexpansive multivalued mappings. J. Glob. Optim. 34, 15–32 (2006) · Zbl 1098.90086 · doi:10.1007/s10898-005-4702-y
[24] Luc, D.T., Tan, N.X.: Existence conditions in variational inclusions with constraints. Optimization 53, 505–515 (2004) · Zbl 1153.49305 · doi:10.1080/02331930412331327175
[25] Noor, M.A., Oettli, W.: On general nonlinear complementarity problems and quasiequilibria. Le Matematiche 49, 313–331 (1994) · Zbl 0839.90124
[26] Tan, N.X.: On the existence of solutions of quasivariational inclusion problems. J. Optim. Theory Appl. 123, 619–638 (2004) · Zbl 1059.49020 · doi:10.1007/s10957-004-5726-z
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