Answers to some open questions on fuzzy ψ-contractions in fuzzy metric spaces

In this paper, we answer two open questions posed by Mihet [Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets Syst. 159 (2008) 739–744] and Gregori et al. [Some questions in fuzzy metric spaces, Fuzzy Sets Syst. 204 (2012) 71–85]. We give a positive answer for the question of Mihet by means of Theorem 1 and a negative answer for the question of Gregori et al. by means of Example 1.