Vector equilibrium type problems with (S)+-conditions

Let X,Y be two Banach spaces, K⊆K be a nonempty set, C⊆Y be a pointed, closed, and convex cone, ϕ :K × K→Y and Φ :K×K×K→Y be two mappings. In this article, we consider the vector equilibrium problem: find x∈K such that for all y∈K, and the extended vector equilibrium problem: find x∈K such that for all y∈K. To study the above problems, we extend the classical (S)+-conditions to vectorial bifunctions. Under (S)+-conditions, we give some existence results for these two problems.