... is said to be G-convex if for each A ∈FD, ΓA⊂ C for all A ⊂ C. For the convenience of our discussion, we also denote ΓA byΓAor ΓNif there is no confusion for A {x0,x1,x2, ,xn}∈FX, ... K. 1.5It is called generalized vector equilibrium problem for short, G VEP , and it has been studiedby many authors; see, for example, 20–22 and references therein. For other possible waysto ... and Fu, y, z ⊂ C for all z ∈Sx. Since Sx is contractible, there exists a continuous mapping h : Sx × 0, 1 → Sxsuch that hs, 0s for all s ∈ Sx and hs, 1u for all s ∈ Sx.Now,wesetHs,...