Khanh, Phan Quoc; Luu, Le Minh Some existence results for vector quasivariational inequalities involving multifunctions and applications to traffic equilibrium problems. (English) Zbl 1097.49012 J. Glob. Optim. 32, No. 4, 551-568 (2005). 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. Cited in 27 Documents 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 PDF BibTeX XML Cite \textit{P. Q. Khanh} and \textit{L. M. Luu}, J. Glob. Optim. 32, No. 4, 551--568 (2005; Zbl 1097.49012) Full Text: DOI OpenURL References: [3] Browder F.E. (1970). Existence theorems for nonlinear partial differential equations. In: Proceedings of Symposia in Pure Mathematics of AMS, Providence, Rhode Island 16, 1–60. · Zbl 0211.17204 [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). 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.