Vectorial Form of Ekeland-Type Variational Principle in Locally Convex Spaces and Its Applications
S Eshghinezhad, M. Fakhar · Fixed Point Theory and Applications · 2010
Abstract By using a Dane"Equation missing"' 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.