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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-3-2,
author = {J. H. Qiu and S. Rolewicz},
title = {Ekeland's variational principle in locally p-convex spaces and related results},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {219-235},
zbl = {1147.46001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-3-2}
}
J. H. Qiu; S. Rolewicz. Ekeland's variational principle in locally p-convex spaces and related results. Studia Mathematica, Tome 187 (2008) pp. 219-235. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-3-2/