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Let X and Y be real Banach spaces, D a nonempty closed convex subset of X, and C:DÃ¢Â†Â’2Y a multifunction such that for each  uÃ¢ÂˆÂˆD, C(u) is a proper, closed and convex cone with intC(u)Ã¢Â‰Â Ã¢ÂˆÂ…,  where intC(u) denotes the interior of C(u). Given the mappings T:DÃ¢Â†Â’2L(X,Y), A:L(X,Y)Ã¢Â†Â’L(X,Y), f:L(X,Y)ÃƒÂ—DÃƒÂ—DÃ¢Â†Â’Y, and h:DÃ¢Â†Â’Y, we study the generalized vector equilibrium-like problem: find u0Ã¢ÂˆÂˆD such that f(As0,u0,v)+h(v)Ã¢ÂˆÂ’h(u0)Ã¢ÂˆÂ‰Ã¢ÂˆÂ’intC(u0) for all vÃ¢ÂˆÂˆD for some s0Ã¢ÂˆÂˆTu0. 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

Generalized Vector Equilibrium-Like Problems without Pseudomonotonicity in Banach Spaces