Eine Ergänzung zum Satz vom abgeschlossenen Wertebereich in lokalkonvexen Räumen.
By modifying the method of Phelps, we obtain a new version of Ekeland's variational principle in the framework of Fréchet spaces, which admits a very general form of perturbations. Moreover we give a density result concerning extremal points of lower semicontinuous functions on Fréchet spaces. Even in the framework of Banach spaces, our result is a proper improvement of the related known result. From this, we derive a new version of Caristi's fixed point theorem and a density result for Caristi...
In the framework of locally p-convex spaces, two versions of Ekeland's variational principle and two versions of Caristi's fixed point theorem are given. It is shown that the four results are mutually equivalent. Moreover, by using the local completeness theory, a p-drop theorem in locally p-convex spaces is proven.