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Journal articles on the topic 'Metric spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 July 2024

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1

Öner, Tarkan, and Alexander Šostak. "Some Remarks on Fuzzy sb-Metric Spaces." Mathematics 8, no. 12 (November 27, 2020): 2123. http://dx.doi.org/10.3390/math8122123.

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Fuzzy strong b-metrics called here by fuzzy sb-metrics, were introduced recently as a fuzzy version of strong b-metrics. It was shown that open balls in fuzzy sb-metric spaces are open in the induced topology (as different from the case of fuzzy b-metric spaces) and thanks to this fact fuzzy sb-metrics have many useful properties common with fuzzy metric spaces which generally may fail to be in the case of fuzzy b-metric spaces. In the present paper, we go further in the research of fuzzy sb-metric spaces. It is shown that the class of fuzzy sb-metric spaces lies strictly between the classes of fuzzy metric and fuzzy b-metric spaces. We prove that the topology induced by a fuzzy sb-metric is metrizable. A characterization of completeness in terms of diameter zero sets in these structures is given. We investigate products and coproducts in the naturally defined category of fuzzy sb-metric spaces.

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2

Fora, Ali Ahmad Ali, Mourad Oqla Massa’deh, and Mohammad Saleh Bataineh. "M-FUZZY METRIC SPACES AND D-METRIC SPACES." Advances in Fuzzy Sets and Systems 21, no. 4 (April 7, 2017): 281–89. http://dx.doi.org/10.17654/fs021040281.

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3

Naidu, S. V. R., K. P. R. Rao, and N. Srinivasa Rao. "On the topology ofD-metric spaces and generation ofD-metric spaces from metric spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 51 (2004): 2719–40. http://dx.doi.org/10.1155/s0161171204311257.

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An example of aD-metric space is given, in whichD-metric convergence does not define a topology and in which a convergent sequence can have infinitely many limits. Certain methods for constructingD-metric spaces from a given metric space are developed and are used in constructing (1) an example of aD-metric space in whichD-metric convergence defines a topology which isT1but not Hausdorff, and (2) an example of aD-metric space in whichD-metric convergence defines a metrizable topology but theD-metric is not continuous even in a single variable.

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4

Isah, Ahmed. "METRICS AND METRIC SPACES OF SOFT MULTISETS." FUDMA JOURNAL OF SCIENCES 7, no. 1 (February 28, 2023): 188–92. http://dx.doi.org/10.33003/fjs-2023-0701-1275.

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The theory of Soft set found applications in so many fields including multiset theory to obtain soft multisets. These theories together with some of their properties were presented. Moreover, considering the various applications of metric spaces in various fields; Metrics and metric spaces of soft multisets with some of their attributes were introduced. However, it was discovered that only pseudo-metric spaces could favorably be formulated. Moreover, soft multiset ordering was also presented.

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5

Nădăban, Sorin. "Fuzzy b-Metric Spaces." International Journal of Computers Communications & Control 11, no. 2 (January 26, 2016): 273. http://dx.doi.org/10.15837/ijccc.2016.2.2443.

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Metric spaces and their various generalizations occur frequently in computer science applications. This is the reason why, in this paper, we introduced and studied the concept of fuzzy b-metric space, generalizing, in this way, both the notion of fuzzy metric space introduced by I. Kramosil and J. Michálek and the concept of b-metric space. On the other hand, we introduced the concept of fuzzy quasi-bmetric space, extending the notion of fuzzy quasi metric space recently introduced by V. Gregori and S. Romaguera. Finally, a decomposition theorem for a fuzzy quasipseudo- b-metric into an ascending family of quasi-pseudo-b-metrics is established. The use of fuzzy b-metric spaces and fuzzy quasi-b-metric spaces in the study of denotational semantics and their applications in control theory will be an important next step.

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6

Li, Changqing, Yanlan Zhang, and Jing Zhang. "On statistical convergence in fuzzy metric spaces." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 3987–93. http://dx.doi.org/10.3233/jifs-200148.

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The idea of statistical convergence, which was first introduced by Fast and Steinhaus independently in 1951, has become one of the most active area of research in the field of mathematics. Recently, it has been applied to the realm of metrics by several authors and some useful results have been obtained. However, the existence of non-completable fuzzy metric spaces, in the sense of George and Veeramani, demonstrates that the theory of fuzzy metrics seem to be richer than that of metrics. In view of this, we attempt to generalize this convergence to the realm of fuzzy metrics. Firstly, we introduce the concept of sts-convergence in fuzzy metric spaces. Then we characterize those fuzzy metric spaces in which all convergent sequences are sts-convergent. Finally, we study sts-Cauchy sequences in fuzzy metric spaces and sts-completeness of fuzzy metric spaces.

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7

BOWDITCH, BRIAN H. "Median and injective metric spaces." Mathematical Proceedings of the Cambridge Philosophical Society 168, no. 1 (July 27, 2018): 43–55. http://dx.doi.org/10.1017/s0305004118000555.

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AbstractWe describe a construction which associates to any median metric space a pseudometric satisfying the binary intersection property for closed balls. Under certain conditions, this implies that the resulting space is, in fact, an injective metric space, bilipschitz equivalent to the original metric. In the course of doing this, we derive a few other facts about median metrics, and the geometry of CAT(0) cube complexes. One motivation for the study of such metrics is that they arise as asymptotic cones of certain naturally occurring spaces.

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8

Wu, Hsien-Chung. "Convergence in Fuzzy Semi-Metric Spaces." Mathematics 6, no. 9 (September 17, 2018): 170. http://dx.doi.org/10.3390/math6090170.

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The convergence using the fuzzy semi-metric and dual fuzzy semi-metric is studied in this paper. The infimum type of dual fuzzy semi-metric and the supremum type of dual fuzzy semi-metric are proposed in this paper. Based on these two types of dual fuzzy semi-metrics, the different types of triangle inequalities can be obtained. We also study the convergence of these two types of dual fuzzy semi-metrics.

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9

Kumam, Poom, Nguyen Van Dung, and Vo Thi Le Hang. "Some Equivalences between Coneb-Metric Spaces andb-Metric Spaces." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/573740.

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We introduce ab-metric on the coneb-metric space and then prove some equivalences between them. As applications, we show that fixed point theorems on coneb-metric spaces can be obtained from fixed point theorems onb-metric spaces.

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10

Oltra, S., S. Romaguera, and E. A. Sánchez-Pérez. "Bicompleting weightable quasi-metric spaces and partial metric spaces." Rendiconti del Circolo Matematico di Palermo 51, no. 1 (February 2002): 151–62. http://dx.doi.org/10.1007/bf02871458.

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11

Tabor, Jacek. "Differential equations in metric spaces." Mathematica Bohemica 127, no. 2 (2002): 353–60. http://dx.doi.org/10.21136/mb.2002.134163.

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12

Aygün, Halis, Elif Güner, Juan-José Miñana, and Oscar Valero. "Fuzzy Partial Metric Spaces and Fixed Point Theorems." Mathematics 10, no. 17 (August 28, 2022): 3092. http://dx.doi.org/10.3390/math10173092.

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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.

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13

Zhu, Yifan, Lu Chen, Yunjun Gao, Baihua Zheng, and Pengfei Wang. "DESIRE." Proceedings of the VLDB Endowment 15, no. 10 (June 2022): 2121–33. http://dx.doi.org/10.14778/3547305.3547317.

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Similarity search finds similar objects for a given query object based on a certain similarity metric. Similarity search in metric spaces has attracted increasing attention, as the metric space can accommodate any type of data and support flexible distance metrics. However, a metric space only models a single data type with a specific similarity metric. In contrast, a multi-metric space combines multiple metric spaces to simultaneously model a variety of data types and a collection of associated similarity metrics. Thus, a multi-metric space is capable of performing similarity search over any combination of metric spaces. Many studies focus on indexing a single metric space, while only a few aims at indexing multi-metric space to accelerate similarity search. In this paper, we propose DESIRE, an efficient dynamic cluster-based forest index for similarity search in multi-metric spaces. DESIRE first selects high-quality centers to cluster objects into compact regions, and then employs B + -trees to effectively index distances between centers and corresponding objects. To support dynamic scenarios, efficient update strategies are developed. Further, we provide filtering techniques to accelerate similarity queries in multi-metric spaces. Extensive experiments on four real datasets demonstrate the superior efficiency and scalability of our proposed DESIRE compared with the state-of-the-art multi-metric space indexes.

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14

Yang, Hui. "Meir–Keeler Fixed-Point Theorems in Tripled Fuzzy Metric Spaces." Mathematics 11, no. 24 (December 14, 2023): 4962. http://dx.doi.org/10.3390/math11244962.

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In this paper, we first propose the concept of a family of quasi-G-metric spaces corresponding to the tripled fuzzy metric spaces (or G-fuzzy metric spaces). Using their properties, we give the characterization of tripled fuzzy metrics. Second, we introduce the notion of generalized fuzzy Meir–Keeler-type contractions in G-fuzzy metric spaces. With the aid of the proposed notion, we show that every orbitally continuous generalized fuzzy Meir–Keeler-type contraction has a unique fixed point in complete G-fuzzy metric spaces. In the end, an example illustrates the validity of our results.

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15

Othman, Khadija Ben, Oliver Von Shtawzen, Ahmad Khaldi, and Rozina Ali. "On Neutrosophic Metric Spaces Generated By Classical Metrics." Galoitica: Journal of Mathematical Structures and Applications 7, no. 1 (2023): 36–42. http://dx.doi.org/10.54216/gjmsa.070104.

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This paper is dedicated to study the concept of symbolic neutrosophic metric spaces and refined neutrosophic metric spaces (X(I),d) which are generated by classical metrics, where many elementary properties will be discussed in terms of theorems and examples. Also, we study the topological properties of neutrosophic open balls, closed balls, and their topological metric complements, with many related examples that clarify the validity of our work.

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16

Ali, Basit, Hammad Ali, Talat Nazir, and Zakaria Ali. "Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces." Mathematics 11, no. 21 (October 26, 2023): 4445. http://dx.doi.org/10.3390/math11214445.

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In order to generalize classical Banach contraction principle in the setup of quasi-metric spaces, we introduce Suzuki-type contractions of quasi-metric spaces and prove some fixed point results. Further, we suggest a correction in the definition of another class of quasi-metrics known as Δ-symmetric quasi-metrics satisfying a weighted symmetry property. We discuss equivalence of various types of completeness of Δ-symmetric quasi-metric spaces. At the end, we consider the existence of fixed points of generalized Suzuki-type contractions of Δ-symmetric quasi-metric spaces. Some examples have been furnished to make sure that generalizations we obtain are the proper ones.

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17

Kato, Hisao. "Scalence metric spaces." Tsukuba Journal of Mathematics 9, no. 1 (June 1985): 143–57. http://dx.doi.org/10.21099/tkbjm/1496160198.

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18

Abobaker, H., and R. Ryan. "Modular Metric Spaces." Irish Mathematical Society Bulletin 0080 (2017): 35–44. http://dx.doi.org/10.33232/bims.0080.35.44.

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19

Gerla, Giangiacomo. "Pointless metric spaces." Journal of Symbolic Logic 55, no. 1 (March 1990): 207–19. http://dx.doi.org/10.2307/2274963.

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In the last years several research projects have been motivated by the problem of constructing the usual geometrical spaces by admitting “regions” and “inclusion” between regions as primitives and by defining the points as suitable sequences or classes of regions (for references see [2]).In this paper we propose and examine a system of axioms for the pointless space theory in which “regions”, “inclusion”, “distance” and “diameter” are assumed as primitives and the concept of point is derived. Such a system extends a system proposed by K. Weihrauch and U. Schreiber in [5].In the sequel R and N denote the set of real numbers and the set of natural numbers, and E is a Euclidean metric space. Moreover, if X is a subset of R, then ⋁X is the least upper bound and ⋀X the greatest lower bound of X.

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20

Zhou, Cai-Li. "Gradual metric spaces." Applied Mathematical Sciences 9 (2015): 689–701. http://dx.doi.org/10.12988/ams.2015.4121017.

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21

Ibragimov, Zair. "Hyperbolizing metric spaces." Proceedings of the American Mathematical Society 139, no. 12 (December 1, 2011): 4401–7. http://dx.doi.org/10.1090/s0002-9939-2011-10857-8.

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22

Hooker, J. N. "Networklike metric spaces." Discrete Mathematics 68, no. 1 (1988): 31–43. http://dx.doi.org/10.1016/0012-365x(88)90039-8.

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23

Panzhensky, V. I., S. E. Stepanov, and M. V. Sorokina. "Metric Affine Spaces." Journal of Mathematical Sciences 245, no. 5 (February 11, 2020): 644–58. http://dx.doi.org/10.1007/s10958-020-04714-3.

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24

Ivanov, A. A. "Weakly metric spaces." Journal of Mathematical Sciences 153, no. 1 (August 2008): 38–42. http://dx.doi.org/10.1007/s10958-008-9116-1.

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25

Mora, G., and D. A. Redtwitz. "Densifiable metric spaces." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 105, no. 1 (February 1, 2011): 71–83. http://dx.doi.org/10.1007/s13398-011-0005-y.

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26

Nekvinda, Aleš, and Ondřej Zindulka. "Monotone Metric Spaces." Order 29, no. 3 (July 20, 2011): 545–58. http://dx.doi.org/10.1007/s11083-011-9221-5.

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27

Bukatin, Michael, Ralph Kopperman, Steve Matthews, and Homeira Pajoohesh. "Partial Metric Spaces." American Mathematical Monthly 116, no. 8 (October 1, 2009): 708–18. http://dx.doi.org/10.4169/193009709x460831.

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28

Kirişci, Murat, and Necip Şimşek. "Neutrosophic metric spaces." Mathematical Sciences 14, no. 3 (June 3, 2020): 241–48. http://dx.doi.org/10.1007/s40096-020-00335-8.

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29

Pajoohesh, H. "k-metric spaces." Algebra universalis 69, no. 1 (December 25, 2012): 27–43. http://dx.doi.org/10.1007/s00012-012-0218-8.

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30

Kuba, Gerald. "Counting metric spaces." Archiv der Mathematik 97, no. 6 (November 24, 2011): 569–78. http://dx.doi.org/10.1007/s00013-011-0328-0.

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31

Xia, Zun-Quan, and Fang-Fang Guo. "Fuzzy metric spaces." Journal of Applied Mathematics and Computing 16, no. 1-2 (March 2004): 371–81. http://dx.doi.org/10.1007/bf02936175.

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32

He, S. Y., L. H. Xie, and P. F. Yan. "On *-metric spaces." Filomat 36, no. 18 (2022): 6173–85. http://dx.doi.org/10.2298/fil2218173h.

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Metric spaces are generalized by many scholars. Recently, Khatami and Mirzavaziri use a mapping called t-definer to popularize the triangle inequality and give a generalization of the notion of a metric, which is called a *-metric. In this paper, we prove that every *-metric space is metrizable. Also, we study the total boundedness and completeness of *-metric spaces.

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33

Anjum, Ansari Shakeel, and Chintaman Tukaram Aage. "Fg-Metric Spaces." European Journal of Mathematics and Statistics 4, no. 2 (March 11, 2023): 1–9. http://dx.doi.org/10.24018/ejmath.2202.4.2.128.

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34

Karapınar, Erdal, and Farshid Khojasteh. "Super metric spaces." Filomat 36, no. 10 (2022): 3545–49. http://dx.doi.org/10.2298/fil2210545k.

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The aim of this paper is to propose a new generalization of metric space which may open a new framework. As an application, we consider the analog of Banach contraction mapping principle that works properly.

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35

Nădăban, Sorin. "Fuzzy quasi-b-metric spaces." Annals of West University of Timisoara - Mathematics and Computer Science 58, no. 2 (December 1, 2022): 38–48. http://dx.doi.org/10.2478/awutm-2022-0015.

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Abstract In this paper we present a new approach for the fuzzy quasi-b-metric spaces and we obtain some properties of these spaces. A special attention is granted to the decomposition theorems of a fuzzy quasi-b-metric into a right continuous and ascending family of quasi-b-metrics. Finally, some future lines of research are highlighted.

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36

Dovgoshey, Oleksiy, and Dmytro Dordovskyi. "Ultrametricity and metric betweenness in tangent spaces to metric spaces." P-Adic Numbers, Ultrametric Analysis, and Applications 2, no. 2 (May 14, 2010): 100–113. http://dx.doi.org/10.1134/s2070046610020020.

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37

Cho, Yeol Je, Keun Saeng Park, and Shih-Sen Chang. "Fixed point theorems in metric spaces and probabilistic metric spaces." International Journal of Mathematics and Mathematical Sciences 19, no. 2 (1996): 243–52. http://dx.doi.org/10.1155/s0161171296000348.

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In this paper, we prove some common fixed point theorems for compatible mappings of type(A)in metric spaces and probabilistic metric spaces Also, we extend Caristi's fixed point theorem and Ekeland's variational principle in metric spaces to probabilistic metric spaces.

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38

Özgür, Nihal Yılmaz, Nabil Mlaiki, Nihal Taş, and Nizar Souayah. "A new generalization of metric spaces: rectangular M-metric spaces." Mathematical Sciences 12, no. 3 (September 2018): 223–33. http://dx.doi.org/10.1007/s40096-018-0262-4.

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39

Paluszyński, Maciej, and Krzysztof Stempak. "On quasi-metric and metric spaces." Proceedings of the American Mathematical Society 137, no. 12 (August 7, 2009): 4307–12. http://dx.doi.org/10.1090/s0002-9939-09-10058-8.

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40

Gautier, Serge, and Karine Pichard. "On metric regularity in metric spaces." Bulletin of the Australian Mathematical Society 67, no. 2 (April 2003): 317–28. http://dx.doi.org/10.1017/s0004972700033785.

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41

Tabatabaie, M. Vojdani, and M. Mahmoudi. "Metric ?-Frames versus Metric Lindelof Spaces." Southeast Asian Bulletin of Mathematics 26, no. 2 (January 2003): 351–61. http://dx.doi.org/10.1007/s100120200056.

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42

Bau, Sheng, and Alan F. Beardon. "The Metric Dimension of Metric Spaces." Computational Methods and Function Theory 13, no. 2 (July 20, 2013): 295–305. http://dx.doi.org/10.1007/s40315-013-0024-0.

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43

Mejía, Diego Alejandro, and Ismael E. Rivera-Madrid. "Absoluteness theorems for arbitrary Polish spaces." Revista Colombiana de Matemáticas 53, no. 2 (July 1, 2019): 109–23. http://dx.doi.org/10.15446/recolma.v53n2.85521.

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By coding Polish metric spaces with metrics on countable sets, we propose an interpretation of Polish metric spaces in models of ZFC and extend Mostowski's classical theorem of absoluteness of analytic sets for any Polish metric space in general. In addition, we prove a general version of Shoenfield's absoluteness theorem.

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44

Shen, Yonghong, Dong Qiu, and Wei Chen. "On Convergence of Fixed Points in Fuzzy Metric Spaces." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/135202.

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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.

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45

Hussain, Nawab, Jamal Rezaei Roshan, Vahid Parvaneh, and Abdul Latif. "A Unification ofG-Metric, Partial Metric, andb-Metric Spaces." Abstract and Applied Analysis 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/180698.

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Using the concepts ofG-metric, partial metric, andb-metric spaces, we define a new concept of generalized partialb-metric space. Topological and structural properties of the new space are investigated and certain fixed point theorems for contractive mappings in such spaces are obtained. Some examples are provided here to illustrate the usability of the obtained results.

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46

Abazari, Rasoul. "Statistical convergence in g-metric spaces." Filomat 36, no. 5 (2022): 1461–68. http://dx.doi.org/10.2298/fil2205461a.

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The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.

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47

Wu, Yaoqiang. "On weak partial-quasi k-metric spaces." Journal of Intelligent & Fuzzy Systems 40, no. 6 (June 21, 2021): 11567–75. http://dx.doi.org/10.3233/jifs-202768.

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In this paper, we introduce the concept of weak partial-quasi k-metrics, which generalizes both k-metric and weak metric. Also, we present some examples to support our results. Furthermore, we obtain some fixed point theorems in weak partial-quasi k-metric spaces.

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48

Kao, Lien-Yung. "Pressure type metrics on spaces of metric graphs." Geometriae Dedicata 187, no. 1 (September 28, 2016): 151–77. http://dx.doi.org/10.1007/s10711-016-0194-9.

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49

CASE, JEFFREY S. "SMOOTH METRIC MEASURE SPACES AND QUASI-EINSTEIN METRICS." International Journal of Mathematics 23, no. 10 (October 2012): 1250110. http://dx.doi.org/10.1142/s0129167x12501108.

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Smooth metric measure spaces have been studied from the two different perspectives of Bakry–Émery and Chang–Gursky–Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Einstein metrics, conformally Einstein metrics, gradient Ricci solitons and static metrics. In this paper, we describe a natural perspective on smooth metric measure spaces from the point of view of conformal geometry and show how it unites these earlier perspectives within a unified framework. We offer many results and interpretations which illustrate the unifying nature of this perspective, including a natural variational characterization of quasi-Einstein metrics as well as some interesting families of examples of such metrics.

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50

Dordovski, Dmitrii V. "Metric tangent spaces to Euclidean spaces." Journal of Mathematical Sciences 179, no. 2 (October 26, 2011): 229–44. http://dx.doi.org/10.1007/s10958-011-0591-4.

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