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

<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>

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

Journal of Applied Research and Technology ◽

10.22201/icat.24486736e.2020.18.1.930 ◽

2020 ◽

Vol 18 (1) ◽

Cited By ~ 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.

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

Journal of Mathematics ◽

10.1155/2020/1712486 ◽

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.

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Some Modified Fixed Point Results in V-Fuzzy Metric Spaces

Advances in Fuzzy Systems ◽

10.1155/2019/6923937 ◽

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.

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Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra-Fredholm Integro-Differential Equations

Mathematics ◽

10.3390/math9161969 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1969

Author(s):

Humaira ◽

Muhammad Sarwar ◽

Thabet Abdeljawad ◽

Nabil Mlaiki

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Upper Bound ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Multivalued Mappings ◽

Contractive Condition ◽

Fuzzy Metric Spaces ◽

Fuzzy Metric

In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative.

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THE PROPERTIES OF OCCASIONALLY WEAKLY COMPATIBLE MAPPING ON FUZZY METRIC SPACES

EDUPEDIA ◽

10.24269/ed.v2i1.87 ◽

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.

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Fixed Point Theorems in Fuzzy Metric Spaces

International Journal of Analysis ◽

10.1155/2013/934145 ◽

2013 ◽

Vol 2013 ◽

pp. 1-4 ◽

Cited By ~ 2

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.

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Some fixed point theorems in fuzzy metric space

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.39.2008.4 ◽

2008 ◽

Vol 39 (4) ◽

pp. 309-316 ◽

Cited By ~ 1

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.

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

Kathmandu University Journal of Science Engineering and Technology ◽

10.3126/kuset.v7i1.5418 ◽

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

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

Advances in Fuzzy Systems ◽

10.1155/2015/285149 ◽

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.

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