Some new fixed point results in non-Archimedean fuzzy metric spaces

In this paper, we introduce the notions of fuzzy (α,β,ϕ)-contractive mapping, fuzzy α-φ-ψ-contractive mapping and fuzzy α-β-contractive mapping and establish some results of fixed point for this class of mappings in the setting of non-Archimedean fuzzy metric spaces. The results presented in this paper generalize and extend some recent results in fuzzy metric spaces. Also, some examples are given to support the usability of our results

Set-valued mappings in partially ordered fuzzy metric spaces

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Fixed point theorems in fuzzy metric spaces

AbstractIn the present work, we establish several fixed point theorems for a new class of self-maps in M-complete fuzzy metric spaces and compact fuzzy metric spaces, respectively

Some questions in fuzzy metric spaces

The George and Veeramani's fuzzy metric defined by $M^*(x,y,t)=\frac{min\{x,y\}+t}{max\{x,y\}+t}$ on $[0,\infty[$ (the set of non-negative real numbers) has shown some advantages in front of classical metrics in the process of filtering images. In this paper we study from the mathematical point of view this fuzzy metric and other fuzzy metrics related to it. As a consequence of this study we introduce, throughout the paper, some questions relative to fuzzy metrics. Also, as another practical application, we show that this fuzzy metric is useful for measuring perceptual colour differences between colour samples.The authors wish to thank both the associated editors coordinating this submission and the reviewers for their insightful suggestions and comments which have been useful to increase the scientific quality and presentation of the paper. Also, the authors thank Dr. M. Melgosa, Dr. R. Huertas and Dr. L. Gomez-Robledo from the Department of Optics of University of Granada, for providing data, information and invaluable comments and suggestions. Valentin Gregori and Samuel Morillas acknowledge the support of Spanish Ministry of Education and Science under Grant MTM 2009-12872-C02-01. Samuel Morillas acknowledges the support of Research Project FIS2010-19839, Ministerio de Educacion y Ciencia (Espana) with European Regional Development Funds (ERDFs).Gregori Gregori, V.; Miñana Prats, JJ.; Morillas Gómez, S. (2012). Some questions in fuzzy metric spaces. Fuzzy Sets and Systems. 204:71-85. https://doi.org/10.1016/j.fss.2011.12.008718520

Contraction mappings in fuzzy quasi-metric spaces and [0,1]-fuzzy posets

[EN] It is well known that each bounded ultraquasi-metric on a set induces, in a natural way, an [0,1]-fuzzy poset. On the other hand, each [0,1]-fuzzy poset can be seen as a stationary fuzzy ultraquasi-metric space for the continuous t-norm Min. By extending this construction to any continuous t-norm, a stationary fuzzy quasi-metric space is obtained. Motivated by these facts, we present several contraction principles on fuzzy quasi-metric spaces that are applied to the class of spaces described above. Some illustrative examples are also given. Finally, we use our approach to deduce in an easy fashion the existence and uniqueness of solution for the recurrence equations typically associated to the analysis of Probabilistic Divide and Conquer Algorithms.The author thanks the support of the Spanish Ministry of Science and Innovation, grand MTM2009-12872-C02-01. The author also thanks the referees because their suggestions and remarks have allowed to improve the first version of this paper.Tirado Peláez, P. (2012). Contraction mappings in fuzzy quasi-metric spaces and [0,1]-fuzzy posets. Fixed Point Theory. 13(1):273-283. http://hdl.handle.net/10251/56871S27328313

On Convergence of Fixed Points in Fuzzy Metric Spaces

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

Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory

Fuzzy Autocatalytic Set (FACS) of fuzzy graph Type-3 is one of the newly capable graphs for a breakthrough of the relationship between fuzzy graph and autocatalytic set. It was successfully used to model an incineration process of a regional clinical waste in 2005. In this research, the mathematical structures of FACS and its properties were explored based on the suitable concept of fuzzy and non-fuzzy metric structure and fuzzy and non-fuzzy normed structure with the structure of its graph. In other words, the possible new structures of FACS have been explored via two new insights of its metric fuzziness and its normed fuzziness. Firstly, a fuzzy detour FT3-distance between vertices in FACS was investigated whereby a quasi-pseudo-FT3-metric fuzziness on FACS which depends on this distance was established, followed by an introduction to the concept FT3-cycle space of FACS as a vector space which is then proven as a normed space. These concepts have led to the visualization of the structure of FACS in a fuzzy norm, hence some propositions and theorems were established. In addition, the study on these structures of FACS was exploited, in particular the connection with functional analysis features and the application of these structures to the clinical incineration process