Abstract
In this paper, we consider more general forms of generalized vector quasi-equilibrium problems for multivalued maps which include many known vector quasi-equilibrium problems and generalized vector quasi-variational inequality problems as special cases. We establish some existence results for solutions of these problems under pseudomonotonicity and u-hemicontinuity/ℓ-hemicontinuity assumptions.
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References
Ansari QH, Flores-Bazán F (2003) Generalized vector quasi-equilibrium problems. J Math Anal Appl 277:246–256
Ansari QH, Yao JC (1999) On strong solutions of the generalized implicit vector variational problem. Adv Nonlinear Variational Inequalitries 2(1):1–10
Ansari QH, Yao JC (2003) Generalized vector equilibrium problems. J Stat Manage Syst 5(1–3):1–17
Ansari QH, Yao JC (2003) On vector quasi-equilibrium problems. In: Daniele P, Giannessi F, Maugeri A (eds) Equilibrium problems and variational models. Kluwer, Dordrecht, pp 1–18
Bianch M, Schaible S (1996) Generalized monotone bifunctions and equilibrium problems. J Optim Theory Appl 90:31–43
Bianch M, Hadjisavvas N, Schaible S (1997) Vector equilibrium problems with generalized monotone bifunctions. J Optim Theory Appl 92:527–542
Blum E, Oettli W (1994) From optimization and variational inequalities to equilibrium problems. Math Stud 63:123–145
Chen GY, Goh CJ, Yang XQ (2001) Existence of solution for generalized vector variational inequalities. Optimization 50:1–15
Chiang Y, Chadli O, Yao JC (2003) Generalized vector equilibrium problems with trifunctions. J Global Optim:1–20
Ding XP, Tarafdar E (2000) Generalized vector variational-like inequalities without monotonicity. In: Giannessi F (ed) Vector variational inequalities and vector equilibria: mathematical theories. Kluwer, Dordrecht, pp 113–124
Flores-Bazan F (2000) Existence theorems for generalized noncoercive equilibrium problems: the quasiconvex case. SIAM J Optim 11:675–690
Flores-Bazan F, Flores-Bazan F (2003) Vector equilibrium problems under asymptotic analysis. J Global Optim 26(2):141–166
Fu JY, Wan AH (2002) Generalized vector equilibria problems with set-valued mappings. Math Methods Oper Res 56:259–268
Giannessi F (1980) Theorems of the alternative, quadratic programs and complementarity problems. In: Cottle RW, Giannessi F, Lions JL (eds) Variational inequalities and complementarity problems. Wiley, New York, pp 151–186
Giannessi F (ed) (2000) Vector variational inequalities and vector equilibria. Mathematical theories. Kluwer, Dordrecht, Boston, London
Hadijisavvas N, Schaible S (1998) From scalar to vector equilibrium problems in the quasi-monotone case. J Optim Theory Appl 96:297–309
Hou SH, Yu H, Chen GY (2003) On vector quasi-equilibrium problems with set-valued maps. J Optim Theory Appl 119:485–498
Khanh PQ, Luu LM (2005) Some existence results for vector quasi-variational inequalities involving multifunctions and applications to traffic equilibrium problems. J Global Optim 32:551–568
Konnov IV, Yao JC (1999) Existence of solutions for generalized vector equilibrium problems. J Math Anal Appl 233, 328–335
Lee GM (2000) On relations between vector varitional inequality and vector optimization problems. In: Yang XQ, Mees AI, Fisher ME, Jennings LS (eds) Progress in optimization. Kluwer, Dordrecht, pp 167–179
Lin LJ (2005) Existence results for prime and dual generalized vector equilibrium problems with applications to generalized semi-infinite programming. J Global Optim 33:579–595
Lin LJ, Park S (1998) On some generalized quasi-equilibrium problems. J Math Anal Appl 224:167–181
Lin LJ, Yu ZT (2001) On some equilibrium problems for multimaps. J Comput Appl Math 129:171–183
Lin LJ, Yu ZT, Ansari QH, Lai LP (2003) Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities. J Math Anal Appl 284:656–671
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Lin, LJ., Ansari, Q.H. & Huang, YJ. Some existence results for solutions of generalized vector quasi-equilibrium problems. Math Meth Oper Res 65, 85–98 (2007). https://doi.org/10.1007/s00186-006-0102-4
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DOI: https://doi.org/10.1007/s00186-006-0102-4
Keywords
- Generalized vector quasi-equilibrium problems
- u-Hemicontinuous
- ℓ-Hemicontinuous
- Quasi-equilibrium problem
- Mixed-variational inequalities
- Upper (lower) semicontinuity
- Pseudomonotone maps