Sensitivity for parametric vector equilibria

In this article, we consider a parametric vector equilibrium problem in topological vector spaces, or metric spaces, if needed, defined as follows: given , find such that where the order in Y is defined by a suitable fixed cone C . We study the upper stability of the map of the solutions S = S (λ), providing results in the peculiar framework of generalized monotone functions. In the particular case of a single-valued solution map, we provide conditions for the Hölder regularity of S in both cases when K is fixed, and also when it depends on a parameter.