scholarly journals Unique Fixed-Point Results in Fuzzy Metric Spaces with an Application to Fredholm Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Iqra Shamas ◽  
Saif Ur Rehman ◽  
Hassen Aydi ◽  
Tayyab Mahmood ◽  
Eskandar Ameer
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Fredholm Integral Equations ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type

This paper aims at proving some unique fixed-point results for different contractive-type self-mappings in fuzzy metric spaces by using the “triangular property of the fuzzy metric”. Some illustrative examples are presented to support our results. Moreover, we present an application by resolving a particular case of a Fredholm integral equation of the second kind.

scholarly journals Fixed Point Theorems via α-ϱ-Fuzzy Contraction

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 69
Author(s):  
Badshah-e- Rome ◽  
Muhammad Sarwar ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type

Some well known results from the existing literature are extended and generalized via new contractive type mappings in fuzzy metric spaces. A non trivial supporting example is also provided to demonstrate the validity of the obtained results.

scholarly journals A Common Fixed Point Theorem in Fuzzy Metric Spaces with Nonlinear Contractive Type Condition Defined Using Φ-Function

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Siniša N. Ješić ◽  
Nataša A. Babačev ◽  
Rale M. Nikolić
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Type Condition ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type ◽  
Common Fixed Point Theorem

This paper is to present a common fixed point theorem for twoR-weakly commuting self-mappings satisfying nonlinear contractive type condition defined using a Φ-function, defined on fuzzy metric spaces. Some comments on previously published results and some examples are given.

scholarly journals Rational Type Fuzzy-Contraction Results in Fuzzy Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Saif Ur Rehman ◽  
Ronnason Chinram ◽  
Chawalit Boonpok
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Type Equation ◽  
Integral Type ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type ◽  
Fuzzy Fixed Point ◽  
Existing Result ◽  
Rational Type

This paper aims to introduce the new concept of rational type fuzzy-contraction mappings in fuzzy metric spaces. We prove some fixed point results under the rational type fuzzy-contraction conditions in fuzzy metric spaces with illustrative examples to support our results. This new concept will play a very important role in the theory of fuzzy fixed point results and can be generalized for different contractive type mappings in the context of fuzzy metric spaces. Moreover, we present an application of a nonlinear integral type equation to get the existing result for a unique solution to support our work.

scholarly journals Control Fuzzy Metric Spaces via Orthogonality with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Fahim Uddin ◽  
Khalil Javed ◽  
Hassen Aydi ◽  
Umar Ishtiaq ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fuzzy Integral ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

In this article, we are generalizing the concept of control fuzzy metric spaces by introducing orthogonal control fuzzy metric spaces. We prove some fixed point results in this setting. We provide nontrivial examples to show the validity of our main results and the introduced concepts. An application to fuzzy integral equations is also included. Our results generalize and improve several developments from the existing literature.

scholarly journals Convex Structure in Generalized Fuzzy Metric Spaces

2021 ◽  
Vol 2 (4) ◽  
pp. 13-16
Author(s):  
M. Jeyaraman ◽  
V. Vinoba ◽  
V. Pazhani
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Convex Structure ◽  
Fuzzy Metric ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper, we introduce the concept of convex structure in generalized fuzzy metric spaces and proved common fixed point theorems for a pair of self-mappings under sufficient contractive type conditions.

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

2021 ◽  
Author(s):  
Hayel N. Saleh ◽  
Mohammad Imdad ◽  
Salvatore Sessa ◽  
Ferdinando Di Martino
Keyword(s):  
Fixed Point ◽  
Fuzzy Sets ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Uniqueness Theorems ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type

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.

scholarly journals Common Fixed Point for Self-Mappings Satisfying an Implicit Lipschitz-Type Condition in Kaleva-Seikkala's Type Fuzzy Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Ming-Liang Song ◽  
Xiu-Juan Zhu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Function Class ◽  
Type Condition ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type ◽  
Common Fixed Point Theorems

We first introduce the new real function classℱsatisfying an implicit Lipschitz-type condition. Then, by usingℱ-type real functions, some common fixed point theorems for a pair of self-mappings satisfying an implicit Lipschitz-type condition in fuzzy metric spaces (in the sense of Kaleva and Seikkala) are established. As applications, we obtain the corresponding common fixed point theorems in metric spaces. Also, some examples are given, which show that there exist mappings which satisfy the conditions in this paper but cannot satisfy the general contractive type conditions.

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 Fixed Point Results for Generalized Fuzzy Contractive Mappings in Fuzzy Metric Spaces with Application in Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Babak Mohammadi ◽  
Azhar Hussain ◽  
Vahid Parvaneh ◽  
Naeem Saleem ◽  
Rogheieh Jalal Shahkoohi
Keyword(s):  
Fixed Point ◽  
Recent Work ◽  
Integral Equations ◽  
Fuzzy Systems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings ◽  
Equivalent Conditions

In this paper, we introduce generalized α - η -fuzzy contractive mappings and generalized β - ζ -fuzzy contractive mappings and prove existence of fixed point for such mappings. Our results generalize and improve the recent work of Gopal and Vetro (Iranian journal of fuzzy systems, 11 (2014), 95–107). Some equivalent conditions of our results are presented. Also, an example is given to support our new results.

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