scholarly journals THE PROPERTIES OF OCCASIONALLY WEAKLY COMPATIBLE MAPPING ON FUZZY METRIC SPACES

EDUPEDIA ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 33
Author(s):  
Citra Rizki ◽  
Sumaji .
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Weakly Compatible ◽  
Compatible Mapping ◽  
Definition Of

In this paper, describe about the properties of occasionally weakly compatible mapping on fuzzy metric spaces in terms of fixed point theory. The discussion of this research is strarted from the concept of fuzzy set and metric space and they were expanded into the concept of fuzzy metric space using continuous norm-t. Furthermore, in investigating about occasionally weakly compatible mapping on fuzzy metric space, we start by given the definition of compatible mapping, weakly commuting, and weakly compatible. Moreover, we construct some theorems to investigating the properties of occasionally weakly compatible mapping on fuzzy metric spaces. 

scholarly journals A Characterization of Strong Completeness in Fuzzy Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 861
Author(s):  
Valentín Gregori ◽  
Juan-José Miñana ◽  
Bernardino Roig ◽  
Almanzor Sapena
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fuzzy Metric Space ◽  
Strong Completeness ◽  
Fuzzy Metric ◽  
Fuzzy Fixed Point ◽  
Nested Sequence

Here, we deal with the concept of fuzzy metric space ( X , M , ∗ ) , due to George and Veeramani. Based on the fuzzy diameter for a subset of X , we introduce the notion of strong fuzzy diameter zero for a family of subsets. Then, we characterize nested sequences of subsets having strong fuzzy diameter zero using their fuzzy diameter. Examples of sequences of subsets which do or do not have strong fuzzy diameter zero are provided. Our main result is the following characterization: a fuzzy metric space is strongly complete if and only if every nested sequence of close subsets which has strong fuzzy diameter zero has a singleton intersection. Moreover, the standard fuzzy metric is studied as a particular case. Finally, this work points out a route of research in fuzzy fixed point theory.

scholarly journals Common fixed point results for various mappings in fuzzy metric spaces with application

2019 ◽  
Vol 38 (5) ◽  
pp. 33-71
Author(s):  
Manish Jain ◽  
Neetu Gupta ◽  
Sanjay Kumar
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
Compatible Mappings ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Weakly Compatible

In this paper, first we discuss the variants of the weakly commuting and compatible mappings in the context of coupled fixed point theory of fuzzy metric spaces. Secondly, we investigate the existence and uniqueness of the common fixed point for pairs of weakly compatible mappings satisfying a new contraction condition in the setup of fuzzy metric spaces with Had i  type t-norm . Further, we talk about some results for the variants of weakly commuting and compatible mappings. At the end, as an application, we obtain metrical version of the discussed results.

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 A Meir-Keeler type fixed point theorem in fuzzy metric spaces

2016 ◽  
Vol 12 (11) ◽  
pp. 6778-6784 ◽  
Author(s):  
Siditë Duraj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Definition Of

In this paper we introduce a new definition of Meir-Keeler type contractions and prove a fixed point theorem for them in fuzzy metric space.

scholarly journals Some Results on Wijsman Ideal Convergence in Intuitionistic Fuzzy Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Ayhan Esi ◽  
Vakeel A. Khan ◽  
Mobeen Ahmad ◽  
Masood Alam
Keyword(s):  
Metric Space ◽  
Cauchy Sequence ◽  
Metric Spaces ◽  
General Setting ◽  
Fuzzy Metric Space ◽  
Ideal Convergence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Closed Sets ◽  
Intuitionistic Fuzzy

In the present work, we study and extend the notion of Wijsman J –convergence and Wijsman J ∗ –convergence for the sequence of closed sets in a more general setting, i.e., in the intuitionistic fuzzy metric spaces (briefly, IFMS). Furthermore, we also examine the concept of Wijsman J ∗ –Cauchy and J –Cauchy sequence in the intuitionistic fuzzy metric space and observe some properties.

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 Points of Eventually Δ-Restrictive and Δ(ϵ)-Restrictive Set-Valued Maps in Metric Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 127 ◽  
Author(s):  
Pradip Debnath ◽  
Manuel de La Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Intrinsic Property ◽  
Point Theory ◽  
Symmetry Principles ◽  
Definition Of ◽  
Metric Function

The symmetry concept is an intrinsic property of metric spaces as the metric function generalizes the notion of distance between two points. There are several remarkable results in science in connection with symmetry principles that can be proved using fixed point arguments. Therefore, fixed point theory and symmetry principles bear significant correlation between them. In this paper, we introduce the new definition of the eventually Δ -restrictive set-valued map together with the concept of p-orbital continuity. Further, we introduce another new concept called the Δ ( ϵ ) -restrictive set-valued map. We establish several fixed point results related to these maps and proofs of these results also provide us with schemes to find a fixed point. In a couple of results, the stronger condition of compactness of the underlying metric space is assumed. Some results are illustrated with examples.

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