Meir–Keeler theorems in fuzzy metric spaces

Zheng, Dingwei; Wang, Pei

doi:10.1016/j.fss.2018.08.014

Cited by 17 publications

(17 citation statements)

References 10 publications

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“…Thereafter, employing a control function satisfying suitable properties, Miheţ [8], and Wardowski [9] generalized the class of fuzzy contractive mapping by introducing the concepts of fuzzy ψ-contractive mapping and fuzzy H-contractive mapping, respectively. For such kind of work, we refer the reader to [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Very recently, Shukla et al gave the concept of fuzzy-Z-contractive, which unify all the classes of mappings mentioned earlier.…”

Section: Introductionmentioning

confidence: 99%

Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings

Saleh¹,

Imdad²,

Sessa³

et al. 2021

Preprint

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In this article, the concept of fuzzy $(\sigma,\mathcal{Z})$-contractive mapping has been introduced in fuzzy metric spaces which is an improvement over the corresponding concept recently introduced by Shukla et al. [Fuzzy Sets and system. 350 (2018) 85--94]. Thereafter, we utilized our newly introduced concept to prove some existence and uniqueness theorems in $\mathcal{M}$-complete fuzzy metric spaces. Our results extend and generalize the corresponding results of Shukla et al.. Moreover, an example is adopted to exhibit the utility of newly obtained results.

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Section: Introductionmentioning

confidence: 99%

Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings

Saleh¹,

Imdad²,

Sessa³

et al. 2021

Preprint

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“…Recently there has been a great interest in discussing some properties on discrete dynamical systems in fuzzy metric spaces. Many authors introduced and investigated the different types of fuzzy contractive maps and obtained a lot of fixed point theorems (see [1,2,5,6,8,11,12,14,15,16,17,18,19]). Until now, there are very little of works that investigates the periodic points of discrete dynamical systems in fuzzy metric spaces because it is much more difficult to find various conditions to obtain the periodic points of discrete dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

The periodic points of ε-contractive maps in fuzzy metric spaces

Sun

Han

et al. 2021

Appl. Gen. Topol.

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<p>In this paper, we introduce the notion of ε-contractive maps in fuzzy metric space (X, M, ∗) and study the periodicities of ε-contractive maps. We show that if (X, M, ∗) is compact and f : X −→ X is ε-contractive, then P(f) = ∩ ∞n=1f n (X) and each connected component of X contains at most one periodic point of f, where P(f) is the set of periodic points of f. Furthermore, we present two examples to illustrate the applicability of the obtained results.</p>

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“…Many authors have studied fuzzy metric spaces (cf. [3,11,13]). In 2004, Park studied the concept of intuitionistic fuzzy metric space with * continuous t-norm and ♦ continuous t-conorm [7].…”

Section: Introductionmentioning

confidence: 99%