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 f : K x K x Lambda --> Y, find (x) over bar is an element of K such that f((x) over bar, y, lambda) not less than 0, for all y is an element of K, 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(lambda), 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 Holder regularity of S in both cases when K is fixed, and also when it depends on a parameter.