Fu, Jun-Yi Symmetric vector quasi-equilibrium problems. (English) Zbl 1031.49013 J. Math. Anal. Appl. 285, No. 2, 708-713 (2003). It is shown that the symmetric vector quasi-equilibrium is solvable under some suitable conditions. As its applications, a coincidence point theorem and the existence of vector optimization problems for a pair of vector-valued functions are obtained. Incidentally, we would like to point out that the symmetric quasi-equilibrium problems were introduced by M. A. Noor and W. Oettlie [“On general nonlinear complementarity problems and quasi-equilibria”, Matematiche 49, 313-331 (1994; Zbl 0839.90124)]. Reviewer: Muhammad Aslam Noor (Sharjah) Cited in 5 ReviewsCited in 28 Documents MSC: 49J40 Variational inequalities 49J53 Set-valued and variational analysis Keywords:equilibrium problems; variational inequalities; existence results Citations:Zbl 0839.90124 PDF BibTeX XML Cite \textit{J.-Y. Fu}, J. Math. Anal. Appl. 285, No. 2, 708--713 (2003; Zbl 1031.49013) Full Text: DOI References: [1] Blum, E.; Oettli, W., From optimization and variational inequalities to equilibrium problems, Math. Student, 63, 123-145 (1994) · Zbl 0888.49007 [2] Fan, K., A minimax inequality and applications, (Shisha, O., Inequalities III (1972), Academic Press: Academic Press New York), 103-113 [3] Ferro, F., A minimax theorem for vector-valued functions, J. Optim. Theory Appl., 60, 19-31 (1989) · Zbl 0631.90077 [4] Fu, J. Y., A vector variational-like inequality for compact acyclic multifunctions and its applications, (Giannessi, F., Vector Variational Inequalities and Vector Equilibria (2000), Kluwer Academic: Kluwer Academic Dordrecht), 141-151 · Zbl 0991.49011 [5] Glicksberg, I., A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points, Proc. Amer. Math. Soc., 3, 170-174 (1952) · Zbl 0046.12103 [6] Jahn, J., Mathematical Vector Optimization in Partially Ordered Linear Spaces (1986), Peter Lang: Peter Lang Frankfurt · Zbl 0578.90048 [7] Noor, M. A.; Oettli, W., On general nonlinear complementarity problems and quasi-equilibria, Le Matematiche, XLIX, 313-331 (1994) · Zbl 0839.90124 [8] Tan, N. X., Quasi-variational inequalities in topological linear locally convex Hausdorff spaces, Math. Nachr., 122, 231-245 (1985) 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.