Ekeland's variational principle in Fréchet spaces and the density of extremal points
Tom 168 / 2005
Studia Mathematica 168 (2005), 81-94
MSC: 49J45, 46A04.
DOI: 10.4064/sm168-1-6
Streszczenie
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 fixed points.
