Existence and duality of generalized \(\epsilon\)-vector equilibrium problems (Q443018)

Summary: We consider a generalized \(\epsilon\)-vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem, we obtain some existence theorems for the generalized \(\epsilon\)-vector equilibrium problem. We also investigate the duality of this generalized \(\epsilon\)-vector equilibrium problem and discuss the equivalence relation between solutions of primal and dual problems.