Generalization Of Drop Theorem And Some Relational Theorems In Locally Convex Spaces

In this paper, two new drop theorems are obtained. One of them is proper improvements of the result which is given by Jing-Hui Qiu and Xi-Yin Zheng by using an instance. Moreover some theorems in relation to drop theorem, which are Phelps' Lemma, Ekeland's Principle and Pareto efficiency theorem due to Isac, are generalized to locally complete locally convex hausdorff spaces.And the equivalence of these theorems is proved. These are the generalization of the work done by A.H.Hamel.In addition, this paper introduced r-drop property,quasi-Ï„-drop property, locally drop property,locally sequentially compact. Applying drop theorem in this paper, it is proved that every Ï„-sequentially compact convex set has the r-drop property, every Ï„-countably compact convex set has the quai-r-drop property and every locally sequentially compact convex set has locally drop property. There conclusions are not only the extension of the result given by Jing-Hui Qiu, but also the simplicity of his way.