Connectedness of approximate solutions set for vector equilibrium problems in Hausdorff topological vector spaces
Bin Chen, Qingyou Liu, Zhibin Liu, Nan‐jing Huang · Fixed Point Theory and Applications · 2011
Abstract In this paper, a scalarization result of ε-weak efficient solution for a vector equilibrium problem (VEP) is given. Using this scalarization result, the connectedness of ε-weak efficient and ε-efficient solutions sets for the VEPs are proved under some suitable conditions in real Hausdorff topological vector spaces. The main results presented in this paper improve and generalize some known results in the literature.