ON GENERALIZATIONS OF EKELAND'S VARIATIONAL PRINCIPLE AND TAKAHASHI'S MINIMIZATION THEOREM AND APPLICATIONS

Abstract

In this paper, we first give a generalization of Takahashi's existence theorem for a vector valued mapping. From the existence theorem, we establish a generalized Caristi's fixed point theorem and a generalized vector Ekeland's variational principle. As an application, we show that if a differentiable function F with values in a Banach lattice has a order lower bound (although it need not attain it), then for every e> 0, there exists some point u_e, where |F(u_e)|<e.