scholarly journals Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 273 ◽  
Author(s):  
Salvador Romaguera ◽  
Pedro Tirado
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Classical Theorem ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Banach Contraction

With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see “Am. Math. Month. 1967, 74, 436–437”) that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see “Fixed Point Theory 2005, 6, 71–78”) also allows us to characterize the fuzzy metric completeness.

scholarly journals Suzuki-Type of Common Fixed Point Theorems in S-Fuzzy Metric Spaces

2021 ◽  
Vol 2 (3) ◽  
pp. 86-91
Author(s):  
M. Jeyaraman ◽  
S. Sowndrarajan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Banach Contraction ◽  
New Type ◽  
Common Fixed Point Theorems

In this paper, by using of Suzuki-type approach [Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136, 1861–1869, 2008.] we prove new type of Suzuki- type fixed point theorem for non-Archimedean S - fuzzy metric spaces which is generalization of Suzuki-Type fixed point results in S - metric spaces.

scholarly journals Multi-valued F-contractions and the solutions of certain functional and integral equations

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1259-1268 ◽  
Author(s):  
Margherita Sgroi ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Banach Contraction

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

scholarly journals On Some Fixed Point Results in E − Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Rachid Mecheraoui ◽  
Zoran D. Mitrović ◽  
Vahid Parvaneh ◽  
Hassen Aydi ◽  
Naeem Saleem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Additional Condition ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
New Class ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem

In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.

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

Mathematics ◽  
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.

scholarly journals On Convergence of Fixed Points in Fuzzy Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yonghong Shen ◽  
Dong Qiu ◽  
Wei Chen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Direction ◽  
Point Theory ◽  
Fuzzy Metric Spaces ◽  
Contraction Mappings ◽  
Fuzzy Metric

We mainly focus on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in fuzzy metric spaces. Our results provide a novel research direction for fixed point theory in fuzzy metric spaces as well as a substantial extension of several important results from classical metric spaces.

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 On the equivalence between Perov fixed point theorem and Banach contraction principle

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3137-3146 ◽  
Author(s):  
Marija Cvetkovic
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Normal Cone ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Theorem ◽  
Banach Contraction

There are many results in the fixed point theory that were presented as generalizations of Banach theorem and other well-known fixed point theorems, but later proved equivalent to these results. In this article we prove that Perov?s existence result follows from Banach theorem by using renormization of normal cone and obtained metric. The observed estimations of approximate point given by Perov, could not be obtained from consequences of Banach theorem on metric spaces.

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