On some triangular inequalities and applications in 2-fuzzy metric spaces

The aim of this paper is to study some level forms of triangular inequality of 2-fuzzy metric spaces which will be useful for application to fixed point problems. For this aim, we first define the concept of 2-fuzzy pre-metric spaces that have weaker axioms than 2-fuzzy metric spaces with the fundamental properties. Then, we investigate the level form inequalities in 2-fuzzy metric spaces equvalent to the triangular inequalities of 2-fuzzy metric spaces by also analyzing the conditions under in which these are provided. Finally, we prove a fixed point theorem for 2-fuzzy metric spaces by considering the obtained level forms of triangular inequalities.Publisher's Versio

An Approach to the Concept of Soft Fuzzy Proximity

The purpose of this paper is to introduce the concept of soft fuzzy proximity. Firstly, we give the definitions of soft fuzzy proximity and Katsaras soft fuzzy proximity, and also we investigate the relations between the soft fuzzy proximity and slightly modified version of Katsaras soft fuzzy proximity. Secondly, we induce a soft fuzzy topology from a given soft fuzzy proximity by using soft fuzzy closure operator. Then, we obtain the initial soft fuzzy proximity from a given family of soft fuzzy proximities. So, we describe products in the category of soft fuzzy proximities. Finally, we show that a family of all soft fuzzy proximities on a given set constitutes a complete lattice

Fuzzy Partial Metric Spaces and Fixed Point Theorems

[EN] 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.This research was funded by Proyecto PGC2018-095709-B-C21 financiado por MCIN/AEI/10.13039/501100011033 y FEDER "Una manera de hacer Europa" and from project BUGWRIGHT2. This last project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreements No. 871260. This publication reflects only the authors' views, and the European Union is not liable for any use that may be made of the information contained therein.Aygün, H.; Güner, E.; Miñana, J.; Valero, O. (2022). Fuzzy Partial Metric Spaces and Fixed Point Theorems. Mathematics. 10(17):1-15. https://doi.org/10.3390/math10173092115101

On Intuitionistic Fuzzy 2-Metric Spaces

In this study, we first recall the notion of an intuitionistic fuzzy 2-metric space and fundamental definitions with several illustrative examples. Then we define the notion of δ−chainable space and (δ,λ)−uniform locally contractive mapping between intuitionistic fuzzy 2-metric spaces. After that, by using the proposed concepts, we obtain a few fixed point theorems of self-mappings defined on this spaces

Evaluation of immunogenicity after first dose of hepatitis B vaccine in newborns with very low birth weight

Objective: Hepatitis-B virus (HBV) infection is an important health problem worldwide. HBV vaccine application varies according to the birth weight and gestational week in the neonatal period. This study aimed to reconsider delaying the administration of the HBV vaccine because the birth weight of newborns was very low. Methods: The newborns with very low birth weight in the study group were babies weighing less than 2000 g in the postnatal first month and at the time of administering HBV vaccine. Babies born at term from mothers who did not receive an HBV vaccine, had negative hepatitis B surface antibody levels, and were given HBV vaccine at birth were included in the study as a control group. The antibody levels against HBV vaccine were compared between these two groups. Results: The retrospective study included 60 participants (32 men and 28 women) grouped as control first vaccine weight (first vaccine weight was >2000 g, control group, n = 30) and case vaccine weight (first vaccine weight was 1500 g groups, respectively. No significant difference was found in hepatitis antibody levels between the groups. Conclusion: Further studies in larger samples are needed to confirm the efficacy and efficiency of postponement of hepatitis B vaccination in babies with a birth weight of <2000 g. © 2021 Taylor & Francis Group, LLC.The authors received no financial support for the research, authorship, and/or publication of this article

Fuzzy Inverse Compactness

We introduce definitions of fuzzy inverse compactness, fuzzy inverse countable compactness, and fuzzy inverse Lindelöfness on arbitrary -fuzzy sets in -fuzzy topological spaces. We prove that the proposed definitions are good extensions of the corresponding concepts in ordinary topology and obtain different characterizations of fuzzy inverse compactness

Antibiotic overconsumption and resistance in Turkey

WOS: 000468097700002PubMed ID: 30844434The latest report of the OECD Health Policy Studies stated that in2015 the highest rates of antimicrobial resistance (around 35% inTurkey, Korea and Greece) were seven times higher than the lowestrates among its member countries. As the OECD country with thehighest rate of resistance (38.8%), despite a 15-year hospital anti-biotic restriction programme, Turkey is in urgent need of revisingits policies and drawing an effective action plan to reverse thecurrent trend. In this commentary we review previous measurestaken to tackle antimicrobial overuse and resistance in Turkey and discuss their effectiveness