Some generalized fixed point theorems for the w-distance were given in [A. Latif
, “Generalized Caristi’s fixed point theorems”, Fixed Point Theory Appl. 2009, Article ID 170140 (2009; Zbl 1171.54031
)]. In the paper under review, it is proved that Latif’s fixed point statements are equivalent with some weak-distance variants of Caristi’s fixed point statement, Ekeland’s variational principle statement and Takahashi’s nonconvex minimization statement.