×

zbMATH — the first resource for mathematics

Stability for parametric implicit vector equilibrium problems. (English) Zbl 1187.90286
Summary: We consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping \(f\) and a set \(K\) are perturbed by parameters \(\epsilon\) and \(\lambda\), respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping \(S\colon\Lambda_1\times\Lambda_2\to 2^X\) for such parametric implicit vector equilibrium problems.

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C31 Sensitivity, stability, parametric optimization
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] 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
[2] Behera, A.; Nayak, L., On nonlinear variational-type inequality problem, Indian J. pure appl. math., 30, 9, 911-923, (1999) · Zbl 0963.49009
[3] Bianchi, M.; Schaible, S., Generalized monotone bifunctions and equilibrium problems, J. optim. theory appl., 90, 1, 31-43, (1996), 92 (8), (1997) 527-542 · Zbl 0903.49006
[4] Blum, E.; Oettli, W., From optimization and variational inequalities to equilibrium problems, Math. student, 63, 123-145, (1994) · Zbl 0888.49007
[5] Chadli, O.; Wong, N.C.; Yao, J.C., Equilibrium problems with applications to eigenvalue problems, J. optim. theory appl., 117, 245-266, (2003) · Zbl 1141.49306
[6] Chen, G.Y.; Yang, Y.Q., Characterizations of variable domination structures via nonlinear scalarization, J. optim. theory appl., 112, 1, 97-110, (2002) · Zbl 0988.49005
[7] ()
[8] Konnov, I., Combined relaxation methods for variational inequalities, (2001), Springer Berlin · Zbl 1044.49004
[9] Ansari, Q.H.; Schaible, S.; Yao, J.C., The system of generalized vector equilibrium problems with applications, J. global optim., 22, 3-16, (2002) · Zbl 1041.90069
[10] Bianchi, M.; Hadjisavvas, N.; Schaible, S., Vector equilibrium problems with generalized monotone bifunctions, J. optim. theory appl., 92, 3, 527-542, (1997) · Zbl 0878.49007
[11] Ding, X.P.; Yao, J.C.; Lin, L.J., Solutions of system of generalized vector quasi-equilibrium problems in locally \(G\)-convex uniform spaces, J. math. anal. appl., 298, 398-410, (2004) · Zbl 1072.49005
[12] Fang, Y.P.; Huang, N.J., Existence results for system of strong implicit vector variational inequalities, Acta math. hungar., 103, 265-277, (2004)
[13] Hadjisavvas, N.; Schaible, S., From scalar to vector equilibrium problems in the quasimonotone case, J. optim. theory appl., 96, 2, 297-309, (1998) · Zbl 0903.90141
[14] Huang, N.J.; Gao, C.J., Some generalized vector variational inequalities and complementarity problems for multivalued mappings, Appl. math. lett., 16, 1003-1010, (2003) · Zbl 1041.49009
[15] Huang, N.J.; Li, J.; Thompson, H.B., Implicit vector equilibrium problems with applications, Math. comput. modelling, 37, 1343-1356, (2003) · Zbl 1080.90086
[16] Li, J.; Huang, N.J.; Kim, J.K., On implicit vector equilibrium problems, J. math. anal. appl., 283, 501-512, (2003) · Zbl 1137.90715
[17] Lin, L.J.; Yu, Z.T.; Kassay, G., Existence of equilibria for multivalued mappings and its application to vectorial equilibria, J. optim. theory appl., 114, 189-208, (2002) · Zbl 1023.49014
[18] Bianchi, M.; Pini, R., A note on stability for parametric equilibrium problems, Oper. res. lett., 31, 445-450, (2003) · Zbl 1112.90082
[19] Li, S.J.; Chen, G.Y.; Teo, K.L., On the stability of generalized vector quasivariational inequality problems, J. optim. theory appl., 113, 283-295, (2002) · Zbl 1003.47049
[20] Aubin, J.P.; Ekeland, I., Applied nonlinear analysis, (1984), John Wiley & Sons New York
[21] Ferro, F., A minimax theorem for vector-valued functions, J. optim. theory appl., 60, 19-31, (1989) · Zbl 0631.90077
[22] Fan, K., A generalization of tychonoff’s fixed point theorem, Math. ann., 142, 305-310, (1961) · Zbl 0093.36701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.