New fuzzy φ -fixed point results employing a new class of fuzzy contractive mappings

Abstract

In this paper, we introduce a new class of fuzzy contractive mappings under the name of ‘ $(F Z, F, φ)$ -contractive mappings’ and utilize the same to prove fuzzy φ-fixed point results. Some illustrative examples are also given to support our results besides deriving several consequences. As an application, we prove an existence and uniqueness result on the solution of first order periodic differential equation. Interestingly, this newly introduced class unifies several known contractions such as: fuzzy contractive, fuzzy ψ-contractive, fuzzy $H$ -contractive and fuzzy $F Z$ -contractive mappings.

Keywords

Fixed point fuzzy metric space

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References

Abbas ,

Imdad and

Gopal , psi– weak contractions in fuzzy metric spaces, Iranian Journal of Fuzzy Systems 8(5) (2011), 141–148.

Altun and

Miheţ , Ordered non-archimedean fuzzy metric spaces and some fixed point results, Fixed Point Theory and Applications 2010(1) (2010), 782680.

Babu ,

Sarma and

Y.G.

Aemro , Generalization of fixed point results for (α, η, β-contractive mappings in fuzzy metric spaces, Bangmod Int J Math & Comp Sci 3(1-2) (2017), 35–52.

D.W.

Boyd and

J.S.

Wong , On nonlinear contractions, Proceedings of the American Mathematical Society 20(2) (1969), 458–464.

George and

Veeramani , On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64(3) (1994), 395–399.

Grabiec , Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27(3) (1988), 385–389.

Gregori and

J.J.

Miñana , Some remarks on fuzzy contractive mappings, Fuzzy Sets and Systems 251 (2014), 101–103.

Gregori and

Sapena , On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125(2) (2002), 245–252.

Jiang ,

Zhan and

Chen , Covering based variable precision (I, T)-fuzzy rough sets with applications to multi-attribute decision-making, IEEE Transactions on Fuzzy Systems (2018). DOI: 10.1109/TFUZZ.2018.2883023

10.

Jleli ,

Samet and

Vetro , Fixed point theory in partial metric spaces via φ-fixed points concept in metric spaces, Journal of Inequalities and Applications 2014(1) (2014), 426.

11.

Kramosil and

Michálek , Fuzzy metrics and statistical metric spaces, Kybernetika 11(5) (1975), 336–344.

12.

Melliani and

Moussaoui , Fixed point theorem using a new class of fuzzy contractive mappings, Journal of Universal Mathematics 1(2) (2018), 148–154.

13.

Miheţ , Fixed point theorems in fuzzy metric spaces using property EA, Nonlinear Analysis: Theory, Methods & Applications 73(7) (2010), 2184–2188.

14.

Miheţ , Fuzzy -contractive mappings in non-archimedean fuzzy metric spaces, Fuzzy Sets and Systems 159(6) (2008), 739–744.

15.

Perveen and

Imdad , Proving new fixed point results in fuzzy metric spaces employing simulation functions, Journal of Intelligence and Fuzzy Systems 36(6) (2019), 6493–6501.

16.

Sangurlu ,

Isik and

Turkoglu , A new method for some fixed point theorems in fuzzy metric spaces, Bangmod Int J Math & Comp Sci 3 (2017), 10–15.

17.

Sangurlu and

Turkoglu , Fixed point theorems for (ψ - ϕ)- contractions in a fuzzy metric spaces, Journal of Nonlinear Sciences and Applications 8(5) (2015), 687–694.

18.

Schweizer and Sklar, Statistical metric spaces, Pacific J Math 10(1) (1960), 313–334.

19.

Sedghi ,

Shobkolaei and

Altun , A new approach to caristi’s fixed point theorem on non-archimedean fuzzy metric spaces, Iranian Journal of Fuzzy Systems 12(2) (2015), 137–143.

20.

Sedghi ,

Shobkolaei ,

Došenović and

Radenović , Suzuki-type of common fixed point theorems in fuzzy metric spaces, Mathematica Slovaca 68(2) (2018), 451–462.

21.

M.S.

Sezen and

Türkoğlu , Some fixed point theorems of (F, φ-fuzzy contractions in fuzzy metric spaces, Journal of Inequalities & Special Functions 8(4) (2017).

22.

Turkoglu and

Sangurlu , Fixed point theorems for fuzzy -contractive mappings in fuzzy metric spaces, Journal of Intelligent & Fuzzy Systems 26(1) (2014), 137–142.

23.

Vu , Existence results for fuzzy volterra integral equation, Journal of Intelligent & Fuzzy Systems 33(1) (2017), 207–213.

24.

Vu ,

L.S.

Dong and

N.N.

Phung , Application of contractivelike mapping principles to impulsive fuzzy functional differential equation, Journal of Intelligent & Fuzzy Systems 33(2) (2017), 753–759.

25.

Wardowski , Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 222 (2013), 108–114.

26.

Zhan ,

Sun and

J.C.R.

Alcantud , Covering based multigranulation (I; T)-fuzzy rough set models and applications in multi-attribute group decision-making, Information Sciences 476 (2019), 290–318.

27.

Zhang ,

Zhan ,

Wu and

J.C.R.

Alcantud , Fuzzy β-covering based (I,T)-fuzzy rough set models and applications to multi-attribute decision-making, Computers & Industrial Engineering 128 (2019), 605–621.

28.

Zhang ,

Zhan and

Xu , Covering-based generalized if rough sets with applications to multi-attribute decision-making, Information Sciences 478 (2019), 275–302.

29.

Zhang ,

Zhan ,

Xu and

J.C.R.

Alcantud , Covering-based general multigranulation intuitionistic fuzzy rough sets and corresponding applications to multi-attribute group decision-making, Information Sciences 494 (2019), 114–140.