Generalized vector equilibrium-like problems without pseudomonotonicity in banach spaces

Let X and Y be real Banach spaces, D a nonempty closed convex subset of X, and C:D→2Y a multifunction such that for each u∈D, C(u) is a proper, closed and convex cone with intC(u)≠∅, where intC(u) denotes the interior of C(u) . Given the mappings T:D→2 L( X,Y), A:L( X,Y)→L( X,Y), f:L( X,Y)×D×D→Y, and h:D→Y, we study the generalized vector equilibrium-like problem: find u0 ∈D such that f( As0,u0,v)+h(v)-h( u0)∉-intC( u0) for all v∈D for some s0 ∈Tu0 . By using the KKM technique and the well-known Nadler result, we prove some existence theorems of solutions for this class of generalized vector equilibrium-like problems. Furthermore, these existence theorems can be applied to derive some existence results of solutions for the generalized vector variational-like inequalities. It is worth pointing out that there are no assumptions of pseudomonotonicity in our existence results.