Some equivalent formulations of the generalized Ekeland’s variational principle and their applications Original Research Article

In this paper, we first give a generalized Takahashi’s existence theorem. From the existence theorem, we establish some equivalence relations between generalized Caristi’s fixed point theorems and generalized Ekeland’s variational principles. Some applications to the existence theorems of weak sharp minima and global error bounds for lower semicontinuous functions are also given.