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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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