Ekeland's variational principle and Caristi's coincidence theorem for set-valued mappings in probabilistic metric spaces (Q5906843)

The authors prove a common generalization of \textit{I. Ekeland's} variational principle [Bull. Am. Math. Soc., New Ser. 1, 443-474 (1979; Zbl 0441.49011)] and \textit{J. Caristi's} coincidence theorem [Trans. Am. Math. Soc. 215, 241-251 (1976; Zbl 0305.47029)] for set-valued mappings in probabilistic metric spaces. They also give a direct proof of the equivalence of these two theorems in probabilistic metric spaces, generalizing a previous result of \textit{S.Z. Shi} [Advan. Math., Beijing, 16, 203-206 (1987; Zbl 0621.54030)].