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Revisiting graphical rectangular b-metric spaces
Asian-European Journal of Mathematics, 2021Very recently, the notion of graphical rectangular [Formula: see text]-metric spaces has been introduced, where the weight of the symmetric edges endowing the directed graph is defined in terms of the underlying metric. Due to its intimate relationship with the directed graphs, such spaces have a wide range of applications in science and engineering ...
Mudasir Younis, Deepak Singh, Luoyi Shi
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Topology and its Applications, 2020
In this paper, the authors introduce the notion of strong partial \(b\)-metric space and establish a number of completion results over such structures. The following are the main results of this exposition. \textbf{Theorem 1.} Every strong partial \(b\)-metric space \((X,\alpha,\sigma)\) admits a \(0\)-Cauchy completion \((X^*,\alpha,\sigma ...
Moshokoa, Seithuti, Ncongwane, Fanyana
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In this paper, the authors introduce the notion of strong partial \(b\)-metric space and establish a number of completion results over such structures. The following are the main results of this exposition. \textbf{Theorem 1.} Every strong partial \(b\)-metric space \((X,\alpha,\sigma)\) admits a \(0\)-Cauchy completion \((X^*,\alpha,\sigma ...
Moshokoa, Seithuti, Ncongwane, Fanyana
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2014
In 1993 another axiom for semimetric spaces, which is weaker than the triangle inequality, was put forth by Czerwik [58] with a view of generalizing the Banach contraction mapping theorem. This same relaxation of the triangle inequality is also discussed in Fagin et al. [79], who call this new distance measure nonlinear elastic matching (NEM).
William Kirk, Naseer Shahzad
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In 1993 another axiom for semimetric spaces, which is weaker than the triangle inequality, was put forth by Czerwik [58] with a view of generalizing the Banach contraction mapping theorem. This same relaxation of the triangle inequality is also discussed in Fagin et al. [79], who call this new distance measure nonlinear elastic matching (NEM).
William Kirk, Naseer Shahzad
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The metrization of rectangular b-metric spaces
Topology and its Applications, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Note on Partial b-Metric Spaces
Mediterranean Journal of Mathematics, 2015Let (X,b) be a partial b-metric space with coefficient $${s \geq 1. \,\,{\rm For \,\, each}\,\, x \in X \,\,{\rm and \,\,each}\,\, \varepsilon > 0, \,\,{\rm put}\,\, B(x, \varepsilon) = \{y \in X \colon b(x,y) 0\}}$$
Xun Ge, Shou Lin
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Orthogonal \(b\)-metric spaces and best proximity points
2022Summary: The aim of this research is to define \(\bot\)-proximally increasing mapping and obtain several best proximity point results concerning this mapping in the framework of new spaces, which is called orthogonal \(b\)-metric spaces. Also, several well-known fixed point results in such spaces are established.
Fallahi, Kamal, Eivani, Shirin
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ON THE COMPLETION OF -METRIC SPACES
Bulletin of the Australian Mathematical Society, 2018Based on the metrisation of$b$-metric spaces of Paluszyński and Stempak [‘On quasi-metric and metric spaces’,Proc. Amer. Math. Soc.137(12) (2009), 4307–4312], we prove that every$b$-metric space has a completion. Our approach resolves the limitation in using the quotient space of equivalence classes of Cauchy sequences to obtain a completion of a$b ...
NGUYEN VAN DUNG, VO THI LE HANG
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The new results in extended \(b\)-metric spaces and applications
2020Mitrovic, Zoran/0000-0001-9993-9082; Isik, Huseyin/0000-0001-7558 ...
Mitrovic, Zoran D. +2 more
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Cauchy sequences in b-metric spaces
Topology and its ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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