In this paper, we obtain the Painleve-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequence of mappings converging in a real locally convex Hausdorff topological vector spaces.
In this paper, minimax theorems and saddle points for a class of vector-valued mappings f（x, y） = u（x） ＋ β（x）v（y） are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.
