DIRECT PROOF OF EKELAND'S PRINCIPLE IN LOCALLY CONVEX HAUSDORFF TOPOLOGICAL VECTOR SPACES

A.H.Hamel proved the Ekeland's principle in a locally convex Hausdorff topological vector spaces by constructing the norm and applying the Ekeland's principle in Banach spaces. In this paper we show that the Ekeland's principle in a locally convex Hausdorff topological vector spaces can be proved directly by applying the famous general principle of H.Br$\acute{e}$zis and F.E.Browder.