A note on vector network equilibrium principles
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- Li, S.J., Yang, X.Q. & Chen, G.Y. Math Meth Oper Res (2006) 64: 327. doi:10.1007/s00186-006-0089-x
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An example is given to show that the necessary conditions of Theorem 4.5 [in Chen et al. Math Methods Oper Res 49:239–253, 1999] and Theorem 2.1 (i) [in Goh and Yang Eur J Oper Res 116:615–628, 1999] for (weak) vector equilibrium flows may not hold. New ξ-equilibrium and parametric equilibrium flows are introduced. As a result, necessary and sufficient conditions between a weak vector equilibrium flow and an ξ-equilibrium flow and between a vector equilibrium flow and a parametric equilibrium flow are established.