A Vectorial Ekeland's Variational Principle on Bornological Vector Spaces

Abstract

We establish a vectorial Ekeland’s variational principle where the objective function is from bornological vector spaces into real vector spaces, and the ordering cone in real vector spaces is not necessarily solid. Meanwhile, a vectorial Caristi’s fixed point theorem and a vectorial Takahashi’s nonconvex minimization theorem are obtained and the equivalences between the three theorems are shown.