A Banach contraction principle in fuzzy metric spaces defined by means of t-conorms

Gregori, Valentı́n; Miñana, Juan-José

doi:10.1007/s13398-021-01068-6

Cited by 4 publications

(3 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The remainder of the paper is devoted to illustrating how such a conclusion allows to prove fixed-point results in fuzzy partial metrics, specifically, those results in which a contractive condition given in the context of fuzzy metrics is established for fuzzy partial metrics. In this context, we present a notion of contractivity in fuzzy metric spaces introduced in [27]. First, let us recall that a binary operation on [0, 1] is called a t-conorm if, for each a, b, c ∈ [0, 1], it satisfies axioms (T1)-(T3) for t-norms given in Definition 2 and additionally the following one:…”

Section: The Main Resultsmentioning

confidence: 99%

“…In [27], the following fixed point theorem was established for fuzzy k--contractions in the context of fuzzy metric spaces. Theorem 4.…”

Section: The Main Resultsmentioning

confidence: 99%

“…Moreover, fixed-point theory in fuzzy metrics shows significant differences when comparing with the classical counterpart (see, for instance, [22][23][24][25][26]). Various recent works are devoted to adapting classical fixed point theorems to the fuzzy metric context (see, for instance, [27][28][29][30][31]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fuzzy Partial Metric Spaces and Fixed Point Theorems

et al. 2022

Self Cite

View full text Add to dashboard Cite

Partial metrics constitute a generalization of classical metrics for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 in order to provide an adequate mathematical framework for the denotational semantics of programming languages. Since then, different works were devoted to obtaining counterparts of metric fixed-point results in the more general context of partial metrics. Nevertheless, in the literature was shown that many of these generalizations are actually obtained as a corollary of their aforementioned classical counterparts. Recently, two fuzzy versions of partial metrics have been introduced in the literature. Such notions may constitute a future framework to extend already established fuzzy metric fixed point results to the partial metric context. The goal of this paper is to retrieve the conclusion drawn in the aforementioned paper by Haghia et al. to the fuzzy partial metric context. To achieve this goal, we construct a fuzzy metric from a fuzzy partial metric. The topology, Cauchy sequences, and completeness associated with this fuzzy metric are studied, and their relationships with the same notions associated to the fuzzy partial metric are provided. Moreover, this fuzzy metric helps us to show that many fixed point results stated in fuzzy metric spaces can be extended directly to the fuzzy partial metric framework. An outstanding difference between our approach and the classical technique introduced by Haghia et al. is shown.

show abstract

Section: The Main Resultsmentioning

confidence: 99%

“…In [27], the following fixed point theorem was established for fuzzy k--contractions in the context of fuzzy metric spaces. Theorem 4.…”

Section: The Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Fuzzy Partial Metric Spaces and Fixed Point Theorems

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

Complexity of the Analysis of Financial Cloud Based on Fuzzy Theory in the Wisdom of Sustainable Urban Development

2021

View full text Add to dashboard Cite

With the rapid growth of our country’s economy, fuzzy theory has become more and more widely used in the financial field. This research mainly explores the application of financial cloud based on fuzzy theory in the sustainable development of smart cities. This research will apply the related knowledge of fuzzy theory, combine the traditional information system risk assessment thought and cloud computing system risk assessment, and propose a series of risk assessment models for the cloud computing system. First, design a smart city model to analyze the potential security issues of the financial cloud computing system. The security level model of cloud computing establishes an index system for evaluation objects based on the level of the security model and uses expert evaluation methods to build models for all levels of the risk profile through the analysis-level process and establish a fuzzy relationship model for each evaluation object value. We objectively evaluate the smart city model based on the designed financial cloud platform. Then, specific statistical analysis is performed on the fuzzy relationship model corresponding to the weight value of the evaluation object, the calculation result is finally obtained, and the risk assessment report of the financial cloud computing system is provided. For every 2% increase in trade dependence, the informatization level of smart cities will drop by about 0.03% on average. The findings have long strengthened the overall coordinated development of the financial system, optimized the financial structure, improved development efficiency, promoted close integration of science and technology and finance, and played the role of government leader it was to fulfill. It shows that we need to maximize it and improve the informatization when building smart cities. The level of development is very important for accelerating urban construction.

show abstract

Aggregation of Fuzzy Metric Spaces: A Fixed Point Theorem

Güner,

Aygün

2024

Wseas Transactions on Mathematics

View full text Add to dashboard Cite

In the last years, fuzzy (quasi-) metric spaces have been used as an important mathematical tool to measure the similarities between the two points with respect to a real parameter. For the reason of the importance of these structures, different kinds of methods have been investigated for use in the applied sciences. So generating new fuzzy (quasi-) metrics from the old ones with aggregation functions has been a research topic. In this paper, we provide a general fixed point theorem using residuum operators for contractions obtained through aggregation functions. We show that there are some necessary conditions and also we provide some examples to show that these conditions cannot be omitted.

show abstract

A Banach contraction principle in fuzzy metric spaces defined by means of t-conorms

Cited by 4 publications

References 22 publications

Fuzzy Partial Metric Spaces and Fixed Point Theorems

Fuzzy Partial Metric Spaces and Fixed Point Theorems

Complexity of the Analysis of Financial Cloud Based on Fuzzy Theory in the Wisdom of Sustainable Urban Development

Aggregation of Fuzzy Metric Spaces: A Fixed Point Theorem

Contact Info

Product

Resources

About