TY - JOUR
ID - 698449
TI - Cauchy Sequences in Fuzzy Metric Spaces and Fixed Point Theorems
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Abtahi, Mortaza
AD - School of Mathematics and Computer Sciences, Damghan University, Damghan, P.O.BOX 36715-364, Iran.
Y1 - 2023
PY - 2023
VL - 20
IS - 1
SP - 137
EP - 152
KW - Fuzzy metric spaces
KW - Cauchy sequences
KW - Fixed point theorems
KW - Contractive mappings
KW - Gauge functions
DO - 10.22130/scma.2022.552400.1099
N2 - In 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.
UR - https://scma.maragheh.ac.ir/article_698449.html
L1 - https://scma.maragheh.ac.ir/article_698449_18116604c0538cf8b0034b8f55d5272a.pdf
ER -