University of MaraghehSahand Communications in Mathematical Analysis2322-580720120230101Cauchy Sequences in Fuzzy Metric Spaces and Fixed Point Theorems13715269844910.22130/scma.2022.552400.1099ENMortazaAbtahiSchool of Mathematics and Computer Sciences, Damghan University, Damghan, P.O.BOX 36715-364, Iran.Journal Article20220515In this paper, contractive mappings of \CM{} type in fuzzy metric spaces are studied. A class $\Psi_1$ of gauge functions $\psi:(0,1]\to(0,1]$ such that, for any $r\in(0,1)$, there exists $\rho\in(r,1)$ such that $1-r> \tau >1-\rho$ implies $\psi(\tau)\geq 1-r$, is introduced, and it is shown that fuzzy $\psi$-contractive mappings are fuzzy contractive mappings of \CM{} type. A characterization of Cauchy sequences in fuzzy metric spaces is presented, and it is utilized to establish fixed point theorems. Examples are given to support the results. Our results cover those of Mihet (Fuzzy $\psi$-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets Syst. 159(2008) 739-744), Wardowski (Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 222(2013) 108-114) and others.https://scma.maragheh.ac.ir/article_698449_18116604c0538cf8b0034b8f55d5272a.pdf