Farajzadeh, A. P.; Amini-Harandi, A.; Kazmi, K. R. Existence of solutions to generalized vector variational-like inequalities. (English) Zbl 1207.90089 J. Optim. Theory Appl. 146, No. 1, 95-104 (2010). The authors provides some existence theorems for generalized vector variational-like inequalities with set-valued mappings in topological vector spaces. They generalize and improve the existing ones in the literature. Reviewer: Fabián Flores-Bazan (Concepción) Cited in 4 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) Keywords:generalized vector variational-like inequalities; C-upper sign-continuous mapping; \(C\)-\(\eta \)-strong pseudomonotone mapping; KKM mapping PDF BibTeX XML Cite \textit{A. P. Farajzadeh} et al., J. Optim. Theory Appl. 146, No. 1, 95--104 (2010; Zbl 1207.90089) Full Text: DOI OpenURL References: [1] Giannessi, F.: Theorem of alternative, quadratic program and complementarity problems. In: Cottle, R.W., Giannessi, F., Lions, J.L. (eds.) Variational Inequality and Complementarity Problems, pp. 151–186. Wiley, New York (1980) · Zbl 0484.90081 [2] Giannessi, F. (ed.): Vector Variational Inequalities and Vector Equilibria, Mathematical Theories. Nonconvex Optimization and Applications, vol. 38. Kluwer Academic, Dordrecht (2000) · Zbl 0952.00009 [3] Giannessi, F., Maugeri, A., Pardalos, P.M. (eds.): Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Methods. Nonconvex Optimization and Its Applications, vol. 58. Kluwer Academic, Dordrecht (2001) · Zbl 0979.00025 [4] Daniele, P., Giannessi, F., Maugeri, A. (eds.): Equilibrium Problems and Variational Models. Including Papers from the Meeting held in Erice, June 23–July 2, 2000. Nonconvex Optimization and Its Applications, vol. 68. Kluwer Academic, Norwell (2003) [5] Chen, G.-Y., Hou, S.H.: Existence of solutions for vector variational inequalities. In: Giannessi, F. (ed.) Vector Variational Inequalities and Vector Equilibria, Mathematical Theories, pp. 73–86. Nonconvex Optimization and Applications, vol. 38. Kluwer Academic, Dordrecht (2000) · Zbl 1012.49007 [6] Fang, Y.-P., Huang, N.-J.: Strong vector variational inequalities in Banach spaces. Appl. Math. Lett. 19, 362–368 (2006) · Zbl 1138.49300 [7] Fang, Y.-P., Huang, N.-J.: Existence results for generalized implicit vector variational inequalities with multivalued mappings. Indian J. Pure Appl. Math. 36, 629–640 (2005) · Zbl 1115.49008 [8] Fang, Y.-P., Huang, N.-J.: Existence results for systems of strong implicit vector variational inequalities. Acta Math. Hung. 103, 265–277 (2004) · Zbl 1060.49003 [9] Kazmi, K.R., Khan, S.A.: Existence of solutions to a generalized system. J. Optim. Theory Appl. 142, 355–361 (2009) · Zbl 1178.49009 [10] Lin, L.-J., Hsu, H.-W.: Existence theorems of systems of vector quasi-equilibrium problems and mathematical programs with equilibrium constraint. J. Glob. Optim. 37, 195–213 (2007) · Zbl 1149.90136 [11] Luc, D.T.: An abstract problem in variational analysis. J. Optim. Theory Appl. 138, 65–76 (2008) · Zbl 1148.49009 [12] Tan, N.X.: Quasi-variational inequalities in topological linear locally convex Hausdorff spaces. Math. Nachr. 122, 231–245 (1985) [13] Ferro, F.: A minimax theorem for vector-valued functions. J. Optim. Theory Appl. 60, 19–31 (1989) · Zbl 0631.90077 [14] Bianchi, M., Pini, R.: Coercivity conditions for equilibrium problems. J. Optim. Theory Appl. 124, 79–92 (2005) · Zbl 1064.49004 [15] Hadjisavvas, N.: Continuity and maximality properties of pseudomonotone operators. J. Convex Anal. 10, 465–475 (2003) · Zbl 1063.47041 [16] Clarke, F.H., Ledyaev, Yu.S., Stern, R.J., Wolenski, P.R.: Nonsmooth Analysis and Control Theory. Springer, Berlin (1998) · Zbl 1047.49500 [17] Yang, X.-Q.: A Hahn-Banach theorem in ordered linear spaces and its applications. Optimization 25, 1–9 (1992) · Zbl 0834.46006 [18] Fan, K.: Some properties of convex sets related to fixed point theorems. Math. Ann. 266, 519–537 (1984) · Zbl 0532.47043 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.