Ekeland's variational principle in locally $p$-convex spaces and related results
Volume 186 / 2008
Studia Mathematica 186 (2008), 219-235
MSC: 46A16, 49J40, 47H10, 49J53.
DOI: 10.4064/sm186-3-2
Abstract
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.
