scholarly journals Common fixed points using (ψ,ϕ ) - type contractive maps in fuzzy metric spaces

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Vishal Gupta ◽  
Manu Verma
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Fuzzy Metric Space ◽  
Contractive Condition ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Control Functions ◽  
Contractive Maps

This In this paper, we define new control functions to give unique fixed point in fuzzy metric space. A fruitful contractive condition of (ψ, ϕ)- type is used to obtain common fixed point theorem for two maps in fuzzy metric spaces. We extend the existing results in metric space to fuzzy metric space using these control functions. The first theorem is the extension of the result of Zhang and Song (2009) under the required contractive conditions. Second result is analogous to the result of Doric (2009) in metric spaces.

scholarly journals Common fixed points for generalized ψ-contractions in weak non-Archimedean fuzzy metric spaces

2019 ◽  
Vol 20 (1) ◽  
pp. 1
Author(s):  
Suthep Suantai ◽  
Yeol Je Cho ◽  
Jukrapong Tiammee
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Linear Equations ◽  
Nonlinear Problems ◽  
Fuzzy Metric Space ◽  
Contractive Condition ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

<p>Fixed point theory in fuzzy metric spaces plays very important role in theory of nonlinear problems in applied science. In this paper, we prove an existence result of common fixed point of four nonlinear mappings satisfying a new type of contractive condition in a generalized fuzzy metric space, called weak non-Archimedean fuzzy metric space. Our main results can be applied to solve the existence of solutions of non-linear equations in fuzzy metric spaces. Some examples supporting our main theorem are also given. Our results improve and generalize some recent results contained in Vetro (2011)[16]to generalized contractive conditions under some suitable conditions and many known results in the literature.</p>

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

2021 ◽  
Vol 22 (2) ◽  
pp. 311
Author(s):  
Taixiang Sun ◽  
Caihong Han ◽  
Guangwang Su ◽  
Bin Qin ◽  
Lue Li
Keyword(s):  
Periodic Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Periodic Points ◽  
Fuzzy Metric Space ◽  
Connected Component ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Maps

<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>

scholarly journals Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Mi Zhou ◽  
Xiao-lan Liu ◽  
Nicolae Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Weak Compatibility ◽  
New Type ◽  
Common Fixed Point Theorems

In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature.

scholarly journals Some Modified Fixed Point Results in V-Fuzzy Metric Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Vishal Gupta ◽  
Manu Verma ◽  
Mohammad Saeed Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Research Paper ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

The present research paper focuses on the existence of fixed point in V-fuzzy metric space. The presentation of V-fuzzy metric space in n-tuple encourages us to define different mapping in the symmetric V-fuzzy metric space. Here, the properties of fuzzy metric space are extended to V-fuzzy metric space. The introduction of notion for pair of mappings (f,g) on V-fuzzy metric space called V-weakly commuting of type Vf and V-R weakly commuting of type Vf is given. This proved fixed point theorem in V-fuzzy metric space employing the effectiveness of E.A. property and CLRg property. For the justification of the results, some examples are illustrated.

scholarly journals Fixed Point Theorems in Fuzzy Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Ismat Beg ◽  
Shaban Sedghi ◽  
Nabi Shobe
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Implicit Relation ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

We prove a fixed point theorem for mappings satisfying an implicit relation in a complete fuzzy metric space.

scholarly journals Some fixed point theorems in fuzzy metric space

2008 ◽  
Vol 39 (4) ◽  
pp. 309-316 ◽  
Author(s):  
Urmila Mishra ◽  
Abhay Sharad Ranadive ◽  
Dhananjay Gopal
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Reciprocal Continuity ◽  
Common Fixed Point Theorems

In this paper we prove common fixed point theorems in fuzzy metric spaces employing the notion of reciprocal continuity. Moreover we have to show that in the context of reciprocal continuity the notion of compatibility and semi-compatibility of maps becomes equivalent. Our result improves recent results of Singh & Jain [13] in the sense that all maps involved in the theorems are discontinuous even at common fixed point.

scholarly journals Some common fixed point theorems in fuzzy metric spaces using compatible of type A-1 and A-2

1970 ◽  
Vol 7 (1) ◽  
pp. 18-27
Author(s):  
CT Aage ◽  
JN Salunke
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Type A ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Common Fixed Point Theorems

Recently M. S Khan, H. K. Pathak and R. George [9] have been introduced the concept of compatible of type A − 1 and type A − 2 and obtained some common fixed point theorems in fuzzy metric spaces. In this connection we have proved some common fixed point theorems in fuzzy metric space using semicompatible mappings. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5418 KUSET 2011; 7(1): 18-27

scholarly journals n-Tupled Fixed Points Theorem in Fuzzy Metric Spaces with Application

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
P. P. Murthy ◽  
Rashmi Kenvat
Keyword(s):  
Fixed Point ◽  
Positive Integer ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type

We will introduce the concept ofn-tupled fixed points (for positive integern) in fuzzy metric space by mild modification of the concept ofn-tupled fixed points (for even positive intergern) introduced by Imdad et al. (2013) in metric spaces. As application of the above-mentioned concept, we will establish somen-tupled fixed point theorems for contractive type mappings in fuzzy metric space which extends the result of Roldán et al. (2013). Also we have given an application to solve a kind of Lipschitzian systems fornvariables and an integral system.

scholarly journals On the local uniqueness of the fixed point of the probabilistic q-contraction in fuzzy metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3453-3458 ◽  
Author(s):  
Olga Hadzic ◽  
Endre Pap
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Local Uniqueness ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

In this paper we prove the local uniqueness of the fixed point of the probabilistic q-contraction in fuzzy metric space.

scholarly journals Pata-Type Fixed-Point Theorems in Kaleva–Seikkala’s Type Fuzzy Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Ao-Lei Sima ◽  
Fei He ◽  
Ning Lu
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Type Contraction

The purpose of this paper is to generalize the fixed-point theorems for Banach–Pata-type contraction and Kannan–Pata-type contraction from metric spaces to Kaleva–Seikkala’s type fuzzy metric spaces. Moreover, two examples are given for the support of our results.

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