Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric space

The main purpose of this paper is to establish the Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric spaces and to give a direct simple proof of the equivalence between these two theorems in the probabilistic metric space. The results presented in this paper generalize the corresponding results of [9–12].The project is supported by National Natural Science Foundation of China.