scholarly journals New Fuzzy Fixed Point Results in Generalized Fuzzy Metric Spaces with Application to Integral Equations

IEEE Access ◽  
2020 ◽  
pp. 1-1
Author(s):  
Muhammad Sohail Ashraf ◽  
Rashid Ali ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Fuzzy Fixed Point

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 Fuzzy fixed point theorems in Hausdorff fuzzy metric spaces

2014 ◽  
Vol 2014 (1) ◽  
pp. 201 ◽  
Author(s):  
Supak Phiangsungnoen ◽  
Wutiphol Sintunavarat ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Fuzzy Fixed Point

Fuzzy relation-theoretic contraction principle

2020 ◽  
pp. 1-11
Author(s):  
Waleed M. Alfaqih ◽  
Based Ali ◽  
Mohammad Imdad ◽  
Salvatore Sessa
Keyword(s):  
Fixed Point ◽  
Fuzzy Sets ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fuzzy Relation ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings ◽  
Fuzzy Fixed Point

In this manuscript, we provide a new and novel generalization of the concept of fuzzy contractive mappings due to Gregori and Sapena [Fuzzy Sets and Systems 125 (2002) 245–252] in the setting of relational fuzzy metric spaces. Our findings possibly pave the way for another direction of relation-theoretic as well as fuzzy fixed point theory. We illustrate several examples to show the usefulness of our proven results. Moreover, we define cyclic fuzzy contractive mappings and utilize our main results to prove a fixed point result for such mappings. Finally, we deduce several results including fuzzy metric, order-theoretic and α-admissible results.

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.

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