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 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.

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 Common fixed point theorems for families of maps in complete L-fuzzy metric spaces

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 67-80 ◽  
Author(s):  
Xianjiu Huang ◽  
Chuanxi Zhu ◽  
Xi Wen
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Mappings ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Common Fixed Point Theorems

In this paper, we prove some common fixed point theorems for any even number of compatible mappings in complete L-fuzzy metric spaces. Our main results extend and generalize some known results in fuzzy metric spaces, intuitionistic metric spaces and L-fuzzy metric spaces.

scholarly journals On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

2021 ◽  
Author(s):  
Mohammad Hussein Mohammad Rashid
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Random Operator ◽  
Random Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings

Abstract In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

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