Department of Mathematics, Faculty of Sciences, University of Isfahan, Isfahan 81745-163, Iran
Academic Editor: A. T M. Lau
Copyright © 2010 S. Eshghinezhad and M. Fakhar. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
By using a Dane' drop theorem in locally convex spaces we obtain a vectorial
form of Ekeland-type variational principle in locally convex spaces. From this theorem,
we derive some versions of vectorial Caristi-Kirk's fixed-point theorem, Takahashi's nonconvex
minimization theorem, and Oettli-Théra's theorem. Furthermore, we show that these
results are equivalent to each other. Also, the existence of solution of vector equilibrium
problem is given.