Existence Theorem Of Efficient Points In Locally Convex Hausdorff Spaces

In this thesis, let E be a locally convex Hausdorff space, and C a. convex cone in E, and≤_c the partial ordering defineded by C. First, the concept of the C-locally complete is defined by≤_c and the relationship of concepts of the locally complete, the C-sequential complete and the C-locally complete are discussed.Next, a existence theorem for the efficient points in locally convex Hausdorff spaces is obtained by using of the properties of the C-locally complete. On the basis of this theorem, we generalize the Phelps lamma and the Ekeland's variational principle in locally convex Hausdorff spaces because the concept of the C-locally complete strictly weaker than the concept of the locally complete. Finally, we establish the Pareto efficiency theorem under the another condition.