In a recent paper Fang (2015)   [1]  , J.X. Fang generalized a crucial fixed point theorem for probabilistic  φ -contractions on complete Menger spaces due to Jachymski (2010)    [3]  . In this note we show that actually Fang's theorem is an easy consequence of Jachymski's theorem. We also observe that the proof of a fixed point theorem for complete metric spaces deduced by Fang from his main result is not correct and present a new proof of it.
['Carmen Alegre', 'Salvador Romaguera']
A note on φ-contractions in probabilistic and fuzzy metric spaces