Kaleva-Seikkala’s Type Fuzzy <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1">
                     <mi>b</mi>
                  </math>-Metric Spaces and Several Contraction Mappings

Li, Shu-fang; He, Fei; Lu, Shu-Min

doi:10.1155/2022/2714912

Cited by 3 publications

(2 citation statements)

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“…Later on, and from the perspective of Kramosil and Michálek, Zhong and Šostak [19] generalized the notion of a fuzzy k-metric space, giving motivating examples and deeply discussing the properties of this new structure. In parallel, various authors have contributed to the development of a theory of a fixed point for these structures (see, e.g., [13,14,[20][21][22][23][24]), while generalizations of the notion of a fuzzy b-metric space to the metric-like and the quasi-metric setting have been initiated and studied in [25,26], respectively.…”

Section: Introductionmentioning

confidence: 99%

Concerning Fuzzy b-Metric Spaces †

Romaguera

2023

Mathematics

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In an article published in 2015, Hussain et al. introduced a notion of a fuzzy b-metric space and obtained some fixed point theorems for this kind of space. Shortly thereafter, Nădăban presented a notion of a fuzzy b-metric space that is slightly different from the one given by Hussain et al., and explored some of its topological properties. Related to Nădăban’s study, Sedghi and Shobe, Saadati, and Šostak independently conducted investigations in articles published in 2012, 2015, and 2018, respectively, about another class of spaces that Sedgi and Shobe called b-fuzzy metric spaces, Saadati, fuzzy metric type spaces, and Šostak, fuzzy k-metric spaces. The main contributions of our paper are the following: First, we propose a notion of fuzzy b-metric space that encompasses and unifies the aforementioned types of spaces. Our approach, which is based on Gabriec’s notion of a fuzzy metric space, allows us to simultaneously cover two interesting classes of spaces, namely, the 01-fuzzy b-metric spaces and the K-stationary fuzzy b-metric spaces. Second, we show that each fuzzy b-metric space, in our sense, admits uniformity with a countable base. From this fact, we derive, among other consequences, that the topology induced by means of its “open” balls is metrizable. Finally, we obtain a characterization of complete fuzzy b-metric spaces with the help of a fixed point result which is also proved here. In support of our approach, several examples, including an application to a type of difference equations, are discussed.

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Section: Introductionmentioning

confidence: 99%

Concerning Fuzzy b-Metric Spaces †

Romaguera

2023

Mathematics

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“…The relation between b-MS and FMS has been discussed by Hassanzadeh and Sedghi [10]. Li et al [11] used Kaleva-Seikkala's type FbMSs and proved several fixed point results by using contraction mappings. Furthermore, Sedghi and Shobe [12,13] proved various common fixed point theorems for R-weakly commuting maps in the framework of FbMSs.…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Results in Controlled Fuzzy Metric Spaces with an Application to the Transformation of Solar Energy to Electric Power

et al. 2023

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In this manuscript, we give sufficient conditions for a sequence to be Cauchy in the context of controlled fuzzy metric space. Furthermore, we generalize the concept of Banach’s contraction principle by utilizing several new contraction conditions and prove several fixed point results. Furthermore, we provide a number of non-trivial examples to validate the superiority of main results in the existing literature. At the end, we discuss an important application to the transformation of solar energy to electric power by utilizing differential equations.

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Fixed point results in controlled revised fuzzy metric spaces with an application to the transformation of solar energy to electric power

Thangathamizh,

Moussaoui,

Došenović

et al. 2024

Vojnotehnički glasnik

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Introduction/purpose: This study establishes sufficient conditions for a sequence to be Cauchy within the framework of controlled revised fuzzy metric spaces. It also generalizes the concept of Banach's contraction principle by introducing several new contraction conditions. The aim is to derive various fixed-point results that enhance the understanding of these mathematical structures. Methods: The researchers employ rigorous mathematical techniques to develop their findings. By defining a set of novel contraction mappings and utilizing properties of controlled revised fuzzy metric spaces, they analyze the implications for sequence convergence. The methodology includes constructing specific examples to illustrate the theoretical results. Results: The study presents several fixed-point theorems derived from the generalized contraction conditions. Additionally, it provides a number of non-trivial examples that substantiate the claims and demonstrate the applicability of the results in practical scenarios. A significant application is explored regarding the conversion of solar energy into electric power, utilizing differential equations to highlight this connection. Conclusion: The findings deepen the understanding of Cauchy sequences in fuzzy metric spaces and offer a broader perspective on the application of the fixed-point theory in real-world scenarios. The results pave the way for further research in both theoretical mathematics and its practical applications, particularly in the field of renewable energy.

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Kaleva-Seikkala’s Type Fuzzy $b$ -Metric Spaces and Several Contraction Mappings

Cited by 3 publications

References 31 publications

Concerning Fuzzy b-Metric Spaces †

Concerning Fuzzy b-Metric Spaces †

Fixed Point Results in Controlled Fuzzy Metric Spaces with an Application to the Transformation of Solar Energy to Electric Power

Fixed point results in controlled revised fuzzy metric spaces with an application to the transformation of solar energy to electric power

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Kaleva-Seikkala’s Type Fuzzy b -Metric Spaces and Several Contraction Mappings

Cited by 3 publications

References 31 publications

Concerning Fuzzy b-Metric Spaces †

Concerning Fuzzy b-Metric Spaces †

Fixed Point Results in Controlled Fuzzy Metric Spaces with an Application to the Transformation of Solar Energy to Electric Power

Fixed point results in controlled revised fuzzy metric spaces with an application to the transformation of solar energy to electric power

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Kaleva-Seikkala’s Type Fuzzy $b$ -Metric Spaces and Several Contraction Mappings