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**Some existence results for vector quasivariational inequalities involving multifunctions and applications to traffic equilibrium problems.**
*(English)*
Zbl 1097.49012

Summary: Some existence results for vector quasivariational inequalities with multifunctions in Banach spaces are derived by employing the KKM-Fan theorem. In particular, we generalize a result by Lin, Yang and Yao, and avoid monotonicity assumptions. We also consider a new quasivariational inequality problem and propose notions of weak and strong equilibria while applying the results to traffic network problems.

### MSC:

49J40 | Variational inequalities |

90C29 | Multi-objective and goal programming |

47J20 | Variational and other types of inequalities involving nonlinear operators (general) |

90B20 | Traffic problems in operations research |

91B52 | Special types of economic equilibria |

### Keywords:

generalized upper or lower hemicontinuity; multifunctions; pseudomonotonicity; traffic networks; upper semicontinuity; vector quasivariational inequalities; weak and strong equilibria
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\textit{P. Q. Khanh} and \textit{L. M. Luu}, J. Glob. Optim. 32, No. 4, 551--568 (2005; Zbl 1097.49012)

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### References:

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[5] | Chen G.Y., Yen N.D. (1993). On the Variational Inequality Model for Network Equilibrium, Internal Report 3.196 (724), Department of Mathematics, University of Pisa. |

[16] | Giannessi F. (1980). Theorems of alternative, quadratic programs and complementarity problems. In: Cottle R.W., Giannessi F., Lions J.-L (eds). Variational Inequalities and Complementarity Problems. Wiley, New York NY, pp. 1–1 · Zbl 0484.90081 |

[17] | Giannessi F. (2000). Vector variational inequalities and vector equilibria, mathematical theories, Vol. 38 of Series. Nonconvex Optimization and its Applications, Kluwer, Dordrecht · Zbl 0952.00009 |

[21] | Hai, N.X. and Khanh, P.Q. (2004), Existence of Solutions to General Quasi-Equilibrium Problems and Applications (In press). |

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