Title of article
Cauchy Sequences in Fuzzy Metric Spaces and Fixed Point Theorems
Author/Authors
Abtahi ، Mortaza School of Mathematics and Computer Sciences - Damghan University
From page
137
To page
152
Abstract
In this paper, contractive mappings of Ćirić-Matkowski type in fuzzy metric spaces are studied. A class Ψ1 of gauge functions ψ : (0, 1] → (0, 1] such that, for any r ∈ (0, 1), there exists ρ ∈ (r, 1) such that 1 − r τ 1 − ρ implies ψ(τ ) ≥ 1 − r, is introduced, and it is shown that fuzzy ψ-contractive mappings are fuzzy contractive mappings of Ćirić-Matkowski 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 ψ-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.
Keywords
Fuzzy metric spaces , Cauchy sequences , Fixed point theorems , Contractive mappings , Gauge functions
Journal title
Sahand Communications in Mathematical Analysis
Journal title
Sahand Communications in Mathematical Analysis
Record number
2735356
Link To Document