Vectorial form of Ekeland-type variational principle in locally convex spaces and its applications

Abstract

By using a Dane s ' 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. Copyright 2010 S. Eshghinezhad and M. Fakhar.