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Journal articles on the topic 'Metric space'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Zhu, Yifan, Lu Chen, Yunjun Gao, Baihua Zheng, and Pengfei Wang. "DESIRE." Proceedings of the VLDB Endowment 15, no. 10 (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

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2

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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3

Jakfar, Muhammad, Manuharawati, Dwi Nur Yunianti, and Mey Dita Kumala. "Metrics on a G-metric Space." Journal of Physics: Conference Series 1417 (December 2019): 012023. http://dx.doi.org/10.1088/1742-6596/1417/1/012023.

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4

Seriu, Masafumi. "Space of Spaces as a Metric Space." Communications in Mathematical Physics 209, no. 2 (2000): 393–405. http://dx.doi.org/10.1007/s002200050025.

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5

Nădăban, Sorin. "Fuzzy b-Metric Spaces." International Journal of Computers Communications & Control 11, no. 2 (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 ascend

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6

Miyachi, Hideki, Ken'ichi Ohshika, and Athanase Papadopoulos. "Tangent spaces of the Teichmüller space of the torus with Thurston's weak metric." Annales Fennici Mathematici 47, no. 1 (2022): 325–34. http://dx.doi.org/10.54330/afm.113702.

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In this paper, we show that the analogue of Thurston's asymmetric metric on the Teichmüller space of flat structures on the torus is weak Finsler and we give a geometric description of its unit circle at each point in the tangent space to Teichmüller space. We then introduce a family of weak Finsler metrics which interpolate between Thurston's asymmetric metric and the Teichmüller metric of the torus (which coincides with the hyperbolic metric). We describe the unit tangent circles of the metrics in this family.

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7

Chen, Peng. "The Metrization Problem in [0,1]-Topology." Mathematics 11, no. 21 (2023): 4430. http://dx.doi.org/10.3390/math11214430.

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This paper discusses the classification of fuzzy metrics based on their continuity conditions, dividing them into Erceg, Deng, Shi, and Chen metrics. It explores the relationships between these types of fuzzy metrics, concluding that a Deng metric in [0,1]-topology must also be Erceg, Chen, and Shi metrics. This paper also proves that the product of countably many Deng pseudo-metric spaces remains a Deng pseudo-metric space, and demonstrates some σ-locally finite properties of Deng metric space. Additionally, this paper constructs two interrelated mappings based on normal space and concludes t

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8

BOWDITCH, BRIAN H. "Median and injective metric spaces." Mathematical Proceedings of the Cambridge Philosophical Society 168, no. 1 (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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Paulraj, Gnanachandra, and X. M. Jeffin Varunnya. "Correlation of Altering JS-Metric with Dislocated Metric." Mapana Journal of Sciences 23, no. 1 (2024): 47–58. https://doi.org/10.12723/mjs.68.3.

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The JS-metric space is a generalized metric space that was first established by Jleli and Samet in the year 2015. We have extended this metric with the aid of altering distance functions and commenced the concept of Altering JS-metric space. Hitzler and Seda introduced the idea of dislocated metric space in the year 2000. In this article, we have examined certain properties of the Altering JS-metric spaces and have discussed the interrelation between the dislocated metric space and the Altering JS-metric space.

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10

Kushwaha, Ramdayal Singh, та Gauree Shanker. "On the ℒ-duality of a Finsler space with exponential metric αeβ/α". Acta Universitatis Sapientiae, Mathematica 10, № 1 (2018): 167–77. http://dx.doi.org/10.2478/ausm-2018-0014.

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Abstract The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.

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11

Rathore, Shilpa, and Dr Abha Tenguria. "Contractive Mapping in Controlled Metric Space and Extended B-Metric Spaces." International Journal of Multidisciplinary Research and Growth Evaluation 6, no. 1 (2025): 1552–61. https://doi.org/10.54660/.ijmrge.2025.6.1.1552-1561.

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This paper discusses contractive mappings in controlled metric spaces and extended b-metric spaces. It starts with setting up the foundational definitions and properties of the mappings of contractive mappings and associated aspects emphasized in terms of their crucial role in ensuring convergence in iterative processes. Investigation is made in controlled metric spaces on how a controlled approach may increase the flexibility and applicability of contractive mappings, specifically in non-standard metrics. This paper extends the ideas developed here further to b-metric spaces where we discuss

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12

Borgaonkar, V. D., K. L. Bondar, and S. M. Jogdand. "COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE." Advances in Mathematics: Scientific Journal 11, no. 1 (2022): 25–34. http://dx.doi.org/10.37418/amsj.11.1.3.

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In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

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13

Vallin. "MORE ON THE METRIC SPACE OF METRICS." Real Analysis Exchange 21, no. 2 (1995): 739. http://dx.doi.org/10.2307/44152685.

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Soni, Bhawna, and Abha Tenguria. "A comparative study of mappings in metric space and controlled metric space." International Journal of Multidisciplinary Research and Growth Evaluation 6, no. 1 (2025): 860–64. https://doi.org/10.54660/.ijmrge.2025.6.1.860-864.

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The objective of this paper is to present a comparative study of mapping in Metric Space and Controlled Metric Space. The study provides the structure, gap analysis and application of Metric Space and Controlled Metric Space. A Comparative Study of Mappings in Metric Space and in Controlled Metric Space is done with the help of studying the concept of metric space, its various types of mappings. Following this, a further conceptualization of Controlled Metric Space with its various types of mappings and its applications is done. A Controlled Metric Space is a specialized concept in Mathematics

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Mohammed Ali, Mayada N., Raghad I. Sabri, and Fatema Ahmad Sadiq. "A new properties of fuzzy b-metric spaces." Indonesian Journal of Electrical Engineering and Computer Science 26, no. 1 (2022): 221. http://dx.doi.org/10.11591/ijeecs.v26.i1.pp221-228.

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Metric <span lang="EN-US">spaces are specific types of topological spaces with pleasing “geometric” characteristics and they have a number of appealing properties and are commonly used in both pure and applied sciences. In this work, the structure of cartesian product space in the setting of a fuzzy b-metric space (Fb-M space) framework is introduced, which is an extension allows to create the large-scale structure for the space of the type fuzzy b-metric. The possibility of transferring some of the results and important features related to Fb-M space to this suggested space are discusse

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16

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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17

ALKURDI, TALEB, SANDER C. HILLE, and ONNO VAN GAANS. "ON METRIZATION OF UNIONS OF FUNCTION SPACES ON DIFFERENT INTERVALS." Journal of the Australian Mathematical Society 92, no. 3 (2012): 281–97. http://dx.doi.org/10.1017/s1446788712000365.

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AbstractThis paper investigates a class of metrics that can be introduced on the set consisting of the union of continuous functions defined on different intervals with values in a fixed metric space, where the union ranges over a family of intervals. Its definition is motivated by the Skorohod metric(s) on càdlàg functions. We show what is essential in transferring the ideas employed in the latter metric to our setting and obtain a general construction for metrics in our case. Next, we define the metric space where elements are sequences of functions from the above mentioned set. We provide c

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18

Yıldız, Filiz, and Nezakat Javanshir. "On the topological locality of antisymmetric connectedness." Filomat 37, no. 12 (2023): 3883–90. http://dx.doi.org/10.2298/fil2312883y.

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The theory of antisymmetric connectedness for a T0-quasi-metric space was established in terms of graph theory lately, as corresponding counterpart of the connectedness for the complement of a graph. Following that in the current study, a topological localized version of the antisymmetrically connected spaces is described and studied through a variety of approaches in the context of T0-quasi-metrics. Within the framework of this, we examine the cases under which conditions a T0-quasi-metric space would become locally antisymmetrically connected as well as some topological characterizations of

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19

Wildrick, K., and T. Zürcher. "Space filling with metric measure spaces." Mathematische Zeitschrift 270, no. 1-2 (2010): 103–31. http://dx.doi.org/10.1007/s00209-010-0787-1.

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20

Ponomarchuk, B. S. "Metric dimension of metric transform and wreath product." Carpathian Mathematical Publications 11, no. 2 (2019): 418–21. http://dx.doi.org/10.15330/cmp.11.2.418-421.

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Let $(X,d)$ be a metric space. A non-empty subset $A$ of the set $X$ is called resolving set of the metric space $(X,d)$ if for two arbitrary not equal points $u,v$ from $X$ there exists an element $a$ from $A$, such that $d(u,a) \neq d(v,a)$. The smallest of cardinalities of resolving subsets of the set $X$ is called the metric dimension $md(X)$ of the metric space $(X,d)$. In general, finding the metric dimension is an NP-hard problem. In this paper, metric dimension for metric transform and wreath product of metric spaces are provided. It is shown that the metric dimension of an arbit

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21

FAVER, TIMOTHY, KATELYNN KOCHALSKI, MATHAV KISHORE MURUGAN, HEIDI VERHEGGEN, ELIZABETH WESSON, and ANTHONY WESTON. "ROUNDNESS PROPERTIES OF ULTRAMETRIC SPACES." Glasgow Mathematical Journal 56, no. 3 (2013): 519–35. http://dx.doi.org/10.1017/s0017089513000438.

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AbstractMotivated by a classical theorem of Schoenberg, we prove that an n + 1 point finite metric space has strict 2-negative type if and only if it can be isometrically embedded in the Euclidean space $\mathbb{R}^{n}$ of dimension n but it cannot be isometrically embedded in any Euclidean space $\mathbb{R}^{r}$ of dimension r < n. We use this result as a technical tool to study ‘roundness’ properties of additive metrics with a particular focus on ultrametrics and leaf metrics. The following conditions are shown to be equivalent for a metric space (X,d): (1) X is ultrametric, (2) X has inf

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22

Rodríuez-Velázquez, Juan. "Lexicographic metric spaces: Basic properties and the metric dimension." Applicable Analysis and Discrete Mathematics 14, no. 1 (2020): 20–32. http://dx.doi.org/10.2298/aadm180627004r.

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In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric dimension of any lexicographic metric space.

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23

Mejía, Diego Alejandro, and Ismael E. Rivera-Madrid. "Absoluteness theorems for arbitrary Polish spaces." Revista Colombiana de Matemáticas 53, no. 2 (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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24

Ali, Mayada Nazar Mohammed, Raghad Ibrahim Sabri, and Fatema Ahmad Sadiq. "A new properties of fuzzy b-metric spaces." Indonesian Journal of Electrical Engineering and Computer Science 26, no. 1 (2022): 221–28. https://doi.org/10.11591/ijeecs.v26.i1.pp221-228.

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Metric spaces are specific types of topological spaces with pleasing “geometric” characteristics and they have a number of appealing properties and are commonly used in both pure and applied sciences. In this work, the structure of cartesian product space in the setting of a fuzzy b-metric space (Fb-M space) framework is introduced, which is an extension allows to create the large-scale structure for the space of the type fuzzy b-metric. The possibility of transferring some of the results and important features related to Fb-M space to this suggested space are discussed and demonst

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25

DAS, Abhishikta, and Tarapada BAG. "A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces." Journal of New Theory, no. 43 (June 30, 2023): 73–82. http://dx.doi.org/10.53570/jnt.1277026.

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This paper contains the equivalence between tvs-G cone metric and G-metric using a scalarization function $\zeta_p$, defined over a locally convex Hausdorff topological vector space. This function ensures that most studies on the existence and uniqueness of fixed-point theorems on G-metric space and tvs-G cone metric spaces are equivalent. We prove the equivalence between the vector-valued version and scalar-valued version of the fixed-point theorems of those spaces. Moreover, we present that if a real Banach space is considered instead of a locally convex Hausdorff space, then the theorems of

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POŞUL, Hande, Çiğdem GÜNDÜZ, and Servet KÜTÜKCÜ. "Soft $A$-Metric Spaces." Journal of New Theory, no. 41 (December 31, 2022): 70–81. http://dx.doi.org/10.53570/jnt.1177525.

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This paper draws on the theory of soft $A$-metric space using soft points of soft sets and the concept of $A$-metric spaces. This new space has great importance as a new type of generalisation of metric spaces since it includes various known metric spaces. In this paper, we introduce the concept of soft $A$-metric space and examine the relations with known spaces. Then, we examine various basic properties of these spaces: soft Hausdorffness, a soft Cauchy sequence, and soft convergence.

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27

Pan, Wenliang, Yujue Li, Jianwu Liu, Pei Dang, and Weixiong Mai. "Metric distributional discrepancy in metric space." Statistics and Its Interface 16, no. 4 (2023): 565–78. http://dx.doi.org/10.4310/22-sii744.

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Rasham, Tahair, Giuseppe Marino, and Abdullah Shoaib. "Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph." Mathematics 7, no. 10 (2019): 884. http://dx.doi.org/10.3390/math7100884.

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Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005–1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F-dominated mappings fulfilling a generalized rational F-dominated contractive condition in the better framework

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Mehrshad, S., and N. Kouhestani. "On pseudo-valuations on BCK-algebras." Filomat 32, no. 12 (2018): 4319–32. http://dx.doi.org/10.2298/fil1812319m.

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In this paper, we study some properties of pseudo-valuations and their induced quasi metrics. The continuity of operation of a BCK-algebra was studied with topology induced by a pseudo-valuation. Moreover, we show that product of finite number of this pseudo metric spaces is a pseudo metric space. Also, we prove that if a BCK-algebra X has a pseudo-valuation, then every quotient space of X has a pseudo metric. The completion of this spaces has been investigated in the present study.

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Masárová, Renáta. "Fréchet Metric for Space of Binary Coded Software." Research Papers Faculty of Materials Science and Technology Slovak University of Technology 22, no. 35 (2014): 17–21. http://dx.doi.org/10.2478/rput-2014-0030.

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Abstract As stated in (7), binary coded computer programs can be shown as a metric space. Therefore, they can be measured by metric in a sense of metric space theory. This paper presents the proof that Fréchet metric is a metric on the space of all sequences of elements M={0,1t} Therefore, it is usable to build a system of software metrics based on the metric space theory

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Şahin, Memet, and Abdullah Kargın. "Neutrosophic Triplet v-Generalized Metric Space." Axioms 7, no. 3 (2018): 67. http://dx.doi.org/10.3390/axioms7030067.

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The notion of Neutrosophic triplet (NT) is a new theory in Neutrosophy. Also, the v‐generalized metric is a specific form of the classical metrics. In this study, we introduced the notion of neutrosophic triplet v‐generalized metric space (NTVGM), and we obtained properties of NTVGM. Also, we showed that NTVGM is different from the classical metric and neutrosophic triplet metric (NTM). Furthermore, we introduced completeness of NTVGM.

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Mennucci, Andrea C. G. "Designing metrics; the delta metric for curves." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 59. http://dx.doi.org/10.1051/cocv/2018044.

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In the first part, we revisit some key notions. Let M be a Riemannian manifold. Let G be a group acting on M. We discuss the relationship between the quotient M∕G, “horizontality” and “normalization”. We discuss the distinction between path-wise invariance and point-wise invariance and how the former positively impacts the design of metrics, in particular for the mathematical and numerical treatment of geodesics. We then discuss a strategy to design metrics with desired properties. In the second part, we prepare methods to normalize some standard group actions on the curve; we design a simple

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33

Narasimhamurthy, S. K., G. N. Latha Kumari та C. S. Bagewadi. "Geometric Properties of Weakly Berwald Space with Some (α,β)-metric". Journal of the Tensor Society 5, № 01 (2007): 1–13. http://dx.doi.org/10.56424/jts.v5i01.10446.

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The (α,β)-metric is a Finsler metric which is contstructed from a Riemann- ian metric (α,β)and a di(α,β)erential 1-form ¯. In this paper Finsler space with some (α,β); ¯)-metrics like L = ((α,β) + ¯)2=(α,β) and L2 = 2(α,β)¯ becomes weakly Berwald spaces under some geometric and algebraic conditions.

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Al-Rawashdeh, Ahmed, Wasfi Shatanawi, and Muna Khandaqji. "Normed Ordered and -Metric Spaces." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/272137.

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In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space , and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of , and we discuss their extension to . We introduce the notion of -metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of convergence and Cauchy theory. In particular, we get a fixed point theorem of a contractive mapping in -metric spaces. Finally, by extending the notion of a contractive sequence in a real-valued metric space, w

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Taş, Nihal, and Nihal Yılmaz Özgür. "On ParametricS-Metric Spaces and Fixed-Point Type Theorems for Expansive Mappings." Journal of Mathematics 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/4746732.

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We introduce the notion of a parametricS-metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametricS-metric space. It is important to obtain new fixed-point theorems on a parametricS-metric space because there exist some parametricS-metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametricS-metric space.

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Myronyk, V., and V. Mykhaylyuk. "DIFFERENT TYPES OF QUASI-METRIC AND PARTIAL METRIC SPACES." Bukovinian Mathematical Journal 11, no. 2 (2023): 211–24. http://dx.doi.org/10.31861/bmj2023.02.21.

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The notion of a partial metric space was introduced by S. Matthews \cite{Matthews1992} in 1992. This notion arose as a certain extension of the notion of metric spaces and was used in computer science, where there are non-Hausdorff topological models. A function $p:X^2\to [0,+\infty)$ is called {\it a partial metric} on $X$ if for all $x,y,z\in X$ the following conditions hold: $(p_1)$ $x=y$ if and only if $p(x,x)=p(x,y)=p(y,y)$; $(p_2)$ $p(x,x)\leq p(x,y)$; $(p_3)$ $p(x,y)=p(y,x)$; \mbox{$(p_4)$ $p(x,z)\leq p(x,y)+p(y,z)-p(y,y)$.} The topology of a partial metric space $(X,p)$ is generated by

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37

Hasanah, Dahliatul. "Fixed Point Theorems in Complex Valued B-Metric Spaces." CAUCHY 4, no. 4 (2017): 138. http://dx.doi.org/10.18860/ca.v4i4.3669.

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A complex-valued b-metric space is a generalization of a b-metric space in which its b-metric space has complex value. It can also be considered as a generalization of a complex-valued metric space. Hence, fixed point theorems that have been studied in b-metric spaces are now of interest whether the theorems are applicable in complex-valued b-metric spaces. In this paper we have obtained some fixed point theorems in complex-valued b-metric spaces. The theorems are derived from the corresponding theorems in b-metric spaces.

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38

Zhao, Fei, and Si Zong Guo. "L_p-Type of Weighted Fuzzy Number Metrics Induced by Fuzzy Structured Element." Advanced Materials Research 981 (July 2014): 279–86. http://dx.doi.org/10.4028/www.scientific.net/amr.981.279.

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For the objective fact that elements with different membership degrees should have different contribution to the metric measure between fuzzy numbers, this paper presents Lp-type of fuzzy number metrics weighted by structured element. Firstly, we define a metric weighted by structured element on the family (B[-1,1]) of all the same monotone and standard bounded functions on closed interval [-1,1] , and discuss the completeness and separability of those metric spaces; Next, using the fuzzy functional induced by normal fuzzy structured element, we give out a method that the metric of the closed

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Furqan, Salman, Naeem Saleem, and Salvatore Sessa. "Fuzzy n−Controlled Metric Space." International Journal of Analysis and Applications 21 (September 18, 2023): 101. http://dx.doi.org/10.28924/2291-8639-21-2023-101.

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This manuscript consists of the idea of n−controlled metric space in fuzzy set theory to generalize a number of fuzzy metric spaces in the literature, for example, pentagonal, hexagonal, triple, and double controlled metric spaces and many other spaces in fuzzy environment. Various examples are given to explain definitions and results. We define open ball, convergence of a sequence and a Cauchy sequence in the context of fuzzy n−controlled metric space. We also prove, by means of an example, that a fuzzy n−controlled metric space is not Hausdorff. At the end of the article, an application is g

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Vasuky, M., and A. Uma. "Convex Fuzzy Soft Metric Space." Shanlax International Journal of Arts, Science and Humanities 7, no. 3 (2020): 78–82. http://dx.doi.org/10.34293/sijash.v7i3.1434.

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In this paper, we investigate the concept of fuzzy soft metric space in terms of fuzzy soft points. The convex structure of fuzzy soft metric spaces is defined and we introduce the convex fuzzy soft metric space. Also we established the fixed point theorem of convex fuzzy soft metric space.

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41

Lei, Yiming, Zhongrui Wang, and Bing Dai. "Metric Dimensions of Metric Spaces over Vector Groups." Mathematics 13, no. 3 (2025): 462. https://doi.org/10.3390/math13030462.

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Let (X,ρ) be a metric space. A subset A of X resolves X if every point x∈X is uniquely identified by the distances ρ(x,a) for all a∈A. The metric dimension of (X,ρ) is the minimum integer k for which a set A of cardinality k resolves X. We consider the metric spaces of Cayley graphs of vector groups over Z. It was shown that for any generating set S of Z, the metric dimension of the metric space X=X(Z,S) is, at most, 2maxS. Thus, X=X(Z,S) can be resolved by a finite set. Let n∈N with n≥2. We show that for any finite generating set S of Zn, the metric space X=X(Zn,S) cannot be resolved by a fin

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42

Sauer, N. W. "Distance Sets of Urysohn Metric Spaces." Canadian Journal of Mathematics 65, no. 1 (2013): 222–40. http://dx.doi.org/10.4153/cjm-2012-022-4.

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Abstract.A metric space M = (M; d) is homogeneous if for every isometry f of a finite subspace of M to a subspace of M there exists an isometry of M onto M extending f . The space M is universal if it isometrically embeds every finite metric space F with dist(F) ⊆ dist(M) (with dist(M) being the set of distances between points in M).A metric space U is a Urysohn metric space if it is homogeneous, universal, separable, and complete. (We deduce as a corollary that a Urysohn metric space U isometrically embeds every separable metric space M with dist(M) ⊆ dist(U).)The main results are: (1) A char

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Shanker, Gauree, and Sarita Rani. "On S-curvature of a homogeneous Finsler space with square metric." International Journal of Geometric Methods in Modern Physics 17, no. 02 (2020): 2050019. http://dx.doi.org/10.1142/s021988782050019x.

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The study of curvature properties of homogeneous Finsler spaces with [Formula: see text]-metrics is one of the central problems in Riemann–Finsler geometry. In this paper, the existence of invariant vector fields on a homogeneous Finsler space with square metric is proved. Further, an explicit formula for [Formula: see text]-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of [Formula: see text]-curvature, the mean Berwald curvature of aforesaid [Formula: see text]-metric is calculated.

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44

Romaguera, Salvador. "Concerning Fuzzy b-Metric Spaces †." Mathematics 11, no. 22 (2023): 4625. http://dx.doi.org/10.3390/math11224625.

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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,

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Sharma, Dileep Kumar, and Jayesh Tiwari. "EXISTENCE AND UNIQUENESS OF COMMON FIXED POINT FOR TWO MAPPINGS IN RECTANGULAR METRIC SPACES AND RECTANGULAR b METRIC SPACES." Jnanabha 51, no. 02 (2021): 120–29. http://dx.doi.org/10.58250/jnanabha.2021.51214.

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The conception of rectangular b-metric space is introduced as a generalization of metric space, b-metric space and rectangular metric space. In this article we present existence and uniqueness of some fixed point results for new contractions in rectangular metric spaces and rectangular b-metric spaces. Some appropriate and innovative examples also displayed to support and validate these new outcomes.

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46

Hosseini, Amin, and Mehdi Mohammadzadeh Karizaki. "On the complex valued metric-like spaces." Filomat 37, no. 15 (2023): 4903–17. http://dx.doi.org/10.2298/fil2315903h.

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The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this article, the concepts such as quasi-equal points, completely separate points, convergence of a sequence, Cauchy sequence, cluster points and complex diameter of a set are defined in a complex valued metric-like space. Moreover, this paper is an attempt to present compatibility definitions for the complex distance between a point and a subset of a complex valued met

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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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48

Mishra, Meera, and R. K. Pandey. "On Randers Change of a Generalized Exponential Metric." InPrime: Indonesian Journal of Pure and Applied Mathematics 6, no. 2 (2024): 194–204. https://doi.org/10.15408/inprime.v6i2.40885.

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In this paper, we study the properties of a special (α, β)-metric e^(k1β/α)+βe^(k2*β/α), the Randers change of the generalized exponential metric. We find the necessary and sufficient condition for this metric to be locally projectively flat and we also prove the conditions for this metric to be of the Berwald and Douglas type.Keywords: Berwald space; Douglas space; Finsler space; -metric; projectively flat. AbstrakPada artikel ini akan dipelajari sifat-sifat khusus dari (α, β) -metric e^(k1β/α)+βe^(k2*β/α), perubahan Randers dari metrik eksponensial umum. Kami menemukan syarat perlu dan cukup

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Hague, Peter R. "A Metric of Solar System Development." New Space 8, no. 1 (2020): 18–22. http://dx.doi.org/10.1089/space.2019.0023.

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Noorwali, Maha, Hamed H. Alsulami, and Erdal Karapınar. "Some Extensions of Fixed Point Results over Quasi-JS-Spaces." Journal of Function Spaces 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/6963041.

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We introduce the notion of quasi-JS-metric space. After defining the basic topological properties of quasi-JS-metric space, we investigate fixed point of certain mapping in the frame of complete quasi-JS-metric space. Our results unify and cover several existing fixed point theorems in distinct structures (such as standard quasi-metric spaces, quasi-b-metric spaces, dislocated quasi-metric spaces, and quasi-modular spaces) in the literature.

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