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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-1-6,
author = {J. H. Qiu},
title = {Ekeland's variational principle in Fr\'echet spaces and the density of extremal points},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {81-94},
zbl = {1061.49013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-1-6}
}
J. H. Qiu. Ekeland's variational principle in Fréchet spaces and the density of extremal points. Studia Mathematica, Tome 166 (2005) pp. 81-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-1-6/