In the present article, inspired by the work of Jleli et al. [J. Inequal. Appl. 2014, 38 (2014)] and [J. Inequal. Appl. 2014, 439 (2014)] in metric spaces, we proposed a new class of contractive mappings termed as: fuzzy Θf-contractive mappings by using an auxiliary function Θf : (0, 1) → (0, 1) satisfying suitable properties. This class has further been weakened by defining the class of fuzzy Θf-weak contractive mappings to realize yet another class of contractive mappings. Thereafter, these two newly introduced classes of contractive mappings are utilized to establish some fixed point theorems in M-complete fuzzy metric spaces (in the sense of George and Veeramani). In support of our newly obtained results, we provide some examples besides furnishing applications to dynamic programming.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
2.
DengZ., Fuzzy pseudo-metric spaces, Journal of Mathematical Analysis and Applications86(1) (1982), 74–95.
3.
ErcegM.A., Metric spaces in fuzzy set theory, Journal of Mathematical Analysis and Applications69(1) (1979), 205–230.
4.
KalevaO. and SeikkalaS., On fuzzy metric spaces, Fuzzy Sets and Systems12(3) (1984), 215–229.
5.
KramosilI. and MichálekJ., Fuzzy metrics and statistical metric spaces, Kybernetika11(5) (1975), 336–344.
6.
GrabiecM., Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems27(3) (1988), 385–389.
7.
FangJ.X., On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems46(1) (1992), 107–113.
8.
GeorgeA. and VeeramaniP., On some results in fuzzy metric spaces, Fuzzy Sets and Systems64(3) (1994), 395–399.
9.
GregoriV. and SapenaA., On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems125(2) (2002), 245–252.
10.
Mihet̆D., Fuzzy ψ-contractive mappings in non-archimedean fuzzy metric spaces, Fuzzy Sets and Systems159(6) (2008), 739–744.
11.
WardowskiD., Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets and Systems222 (2013), 108–114.
12.
ShuklaS., GopalD. and SintunavaratW., A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets and Systems350 (2018), 85–94.
13.
MellianiS. and MoussaouiA., Fixed point theorem using a new class of fuzzy contractive mappings, Journal of Universal Mathematics1(2) (2018), 148–154.
14.
TiradoP., Contraction mappings in fuzzy quasi-metric spaces and [0, 1]-fuzzy posets, Fixed Point Theory13(1) (2012), 273–283.
15.
SangurluM. and TurkogluD., Fixed point theorems for (ψ ∘ φ)-contractions in a fuzzy metric spaces, Journal of Nonlinear Sciences and Applications8(5) (2015), 687–694.
16.
ShenY., QiuD. and ChenW., Fixed point theorems in fuzzy metric spaces, Applied Mathematics Letters25(2) (2012), 138–141.
17.
SalehH.N., KhanI.A., ImdadM. and AlfaqihW.M., New fuzzy ϕ-fixed point results employing a new class of fuzzy contractive mappings, Journal of Intelligent & Fuzzy Systems37(4) (2019), 5391–5402.
18.
PerveenA. and ImdadM., Proving new fixed point results in fuzzy metric spaces employing simulation function, Journal of Intelligent & Fuzzy Systems36(6) (2019), 6493–6501.
19.
VuH., Existence results for fuzzy volterra integral equation, Journal of Intelligent & Fuzzy Systems33(1) (2017), 207–213.
20.
RakićD., DošenovićT., MitrovićZ.D., de la SenM. and RadenovićS., Some fixed point theorems of ćirić type in fuzzy metric spaces, Mathematics8(2) (2020), 297.
21.
ImdadM. and AliJ., Some common fixed point theorems in fuzzy metric spaces, Mathematical Communications11(2) (2006), 153–163.
22.
ImdadM., AliJ. and HasanM., Common fixed point theorems in fuzzy metric spaces employing common property (EA), Mathematical and Computer Modelling55(3-4) (2012), 770–778.
23.
SedghiS., ShobkolaeiN., DošenovićT. and RadenovićS., Suzuki-type of common fixed point theorems in fuzzy metric spaces, Mathematica Slovaca68(2) (2018), 451–462.
24.
GuptaV., DeepR. and TripathiA.K., Some common fixed point theorems in fuzzy metric spaces and their applications, Boletim da Sociedade Paranaense de Matemática36(3) (2018), 141–153.
25.
GopalD. and ImdadM., Some new common fixed point theorems in fuzzy metric spaces, Annali delĺ Universitá di Ferrara57(2) (2011), 303–316.
26.
JleliM. and SametB., A new generalization of the Banach contraction principle, Journal of Inequalities and Applications2014(1) (2014), 38.
27.
JleliM., KarapınarE. and SametB., Further generalizations of the Banach contraction principle, Journal of Inequalities and Applications2014(1) (2014), 439.
BabuG., SarmaK. and AemroY.G., Generalization of fixed point results for (α, η, β)-contractive mappings in fuzzy metric spaces, Bangmod Int J Math & Comp Sci3(1-2) (2017), 35–52.
