In this paper,we obtain the Painlev'e-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 vectorvalued mappings.
