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Gap functions and existence of solutions to generalized vector quasi-equilibrium problems. (English) Zbl 1090.49014

Summary: This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established.

MSC:

49J40 Variational inequalities
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References:

[5] Chen, G.Y., Yang, X.Q. and Yu, H. (2004), A nonlinear scalarization function and generalized quasi-vector equilibrium problems, Journal of Global Optimization. In press, available online. · Zbl 1130.90413
[11] Li, S.J., Teo, K.L. and Yang, X.Q., On generalized vector quasi-equilibrium problems,preprint. · Zbl 1170.90478
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