Generalized vector variational‐like inequalities and vector optimization

In this paper, we consider different kinds of generalized vector variational‐like inequality problems and a vector optimization problem. We establish some relationships between the solutions of generalized Minty vector variational‐like inequality problem and an efficient solution of a vector optimization problem. We define a perturbed generalized Stampacchia vector variational‐like inequality problem and discuss its relation with generalized weak Minty vector variational‐like inequality problem. We establish some existence results for solutions of our generalized vector variational‐like inequality problems.