Optimality Conditions Of Solutions To Vector Equilibrium Problems

In this paper, first of all, we study the optimality conditions for weak efficient solution, Henig efficient solution, globally efficient solution and superefficient solution to the convex-like vector equilibrium problems with constraints, and present an example to illustrate convex-like is weaker than convex. As application,we provide sufficient and necessary conditions for weak efficient solution, Henig efficient solution, globally efficient solution and superefficient solution to the vector optimalization problems. Then, We introduce the concepts ofε-efficient solution,ε-Henig efficient solution,ε-globally efficient solution of vetor equilibrium problems without constraints in Banach spaces, and provide sufficient and necessary conditions forε-efficient solution,ε-weak efficient solution,ε-Henig efficient solution andε-globally efficient solution to the vetor equilibrium problems without constraints. As applications,we provide sufficient and necessary conditions forε-efficient solution,ε-weak efficient solution,ε-Henig efficient solution,ε-globally efficient solution to the vector variational inequalities and vector optimalization problems.