On fuzzy contractive mappings in fuzzy metric spaces

Some results on fuzzy contractive mappings in [V. Gregori, A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002) 245–253] are extended to Edelstein fuzzy contractive mappings. Some new results are obtained by modifying the notion of convergence in fuzzy metric spaces. Due to specific axiom (GV-2), in fuzzy metric spaces in the sense of George and Veeramani this convergence is Fréchet.