This paper deals with some issues of fixed point concerning Caristi type mappings introduced by Abbasi and Golshan (Kybernetika 52:929–942, 2016) in fuzzy metric spaces. We enlarge this class prove completeness characterization corresponding space. The includes a comprehensive set examples showing the generality our results an open question.

With a recent result of Suzuki 2001 we extend Caristi-Kirk’s fixed point theorem, Ekeland’s variational principle, and Takahashi’s minimization theorem in a complete metric space by replacing the distance with a τ-distance. In addition, these extensions are shown to be equivalent. When the τ-distance is l.s.c. in its second variable, they are applicable to establish more equivalent results abou...