Connectedness and path-connectedness of solution sets to symmetric vector equilibrium problems. (English) Zbl 1176.49019
Summary: We study the connectedness and path-connectedness of the solution sets for symmetric vector equilibrium problems in locally convex Hausdorff topological vector spaces under some suitable assumptions. The results presented in this paper generalize some known results in [B. Chen, X. H. Gong and S. M. Yuan, J. Inequal. Appl. 2008, Article ID 581849, 15 p. (2008; Zbl 1157.49009); Y. H. Cheng, J. Math. Anal. Appl. 260, No.1, 1-5 (2001; Zbl 0990.49010); X. H. Gong, J. Optim. Theory Appl. 133, No. 2, 151–161 (2007; Zbl 1155.90018); G. M. Lee, D. S. Kim, B. S. Lee and N. D. Yen, Nonlinear Anal., Theory Methods Appl. 34, No. 5, 745–765 (1998; Zbl 0956.49007); G. M. Lee and I. J. Bu, Nonlinear Anal. 63, 1847–1855 (2005)].
