On the topology of D-metric spaces and generation of D-metric spaces from metric spaces by S. V. R. Naidu, K. P. R. Rao, N. Srinivasa Rao

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Fixed point theorems in metric spaces and probabilistic metric spaces by Yeol Je Cho, Keun Saeng Park, Shih-Sen Chang

“…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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Some Equivalences between Cone b-Metric Spaces and b-Metric Spaces by Poom Kumam, Nguyen Van Dung, Vo Thi Le Hang

“…As applications, we show that fixed point theorems on cone b-metric spaces can be obtained from fixed point theorems on b-metric spaces.…”
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Cyclic Contractions on -Metric Spaces by E. Karapınar, A. Yıldız-Ulus, İ. M. Erhan

“…Conditions for existence and uniqueness of fixed points of two types of cyclic contractions defined on -metric spaces are established and some illustrative examples are given. …”
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Ordered Convex Metric Spaces by Ismat Beg

“…The aim of this article is to introduce a new notion of ordered convex metric spaces and study some basic properties of these spaces. …”
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On Controlled Rectangular Metric Spaces and an Application by Nayab Alamgir, Quanita Kiran, Hassen Aydi, Yaé Ulrich Gaba

“…In this paper, we introduce the notion of controlled rectangular metric spaces as a generalization of rectangular metric spaces and rectangular b-metric spaces. …”
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Normed Ordered and 𝐸-Metric Spaces by Ahmed Al-Rawashdeh, Wasfi Shatanawi, Muna Khandaqji

“…We introduce the notion of 𝐸-metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of convergence and Cauchy theory. …”
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On Ćirić-Prešić Operators in Metric Spaces by Narongsuk Boonsri, Satit Saejung, Kittipong Sitthikul

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On Neutrosophic 2-Metric Spaces with Application by Ali Asghar, Aftab Hussain, Khaleel Ahmad, Umar Ishtiaq, Hamed Al Sulami, Nawab Hussain

“…The goal of this manuscript is to present the notion of neutrosophic 2-metric spaces. In this situation, we prove various fixed point theorems. …”
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Peano compactifications and property S metric spaces by R. F. Dickman

“…Let (X,d) denote a locally connected, connected separable metric space. We say the X is S-metrizable provided there is a topologically equivalent metric ρ on X such that (X,ρ) has Property S, i.e. for any ϵ>0, X is the union of finitely many connected sets of ρ-diameter less than ϵ. …”
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Hyperbolic Metric Spaces and Stochastic Embeddings by Chris Gartland

“…Stochastic embeddings of finite metric spaces into graph-theoretic trees have proven to be a vital tool for constructing approximation algorithms in theoretical computer science. …”
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New Contributions in Generalization S-Metric Spaces to S∗p-Partial Metric Spaces with Some Results in Common Fixed Point Theorems by Asma Al Rwaily, A. M. Zidan

“…In this paper, we introduce the notion of S∗p-partial metric spaces which is a generalization of S-metric spaces and partial-metric spaces. …”
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On Fixed Point Results in Controlled Metric Spaces by Jamshaid Ahmad, Abdullah Eqal Al-Mazrooei, Hassen Aydi, Manuel De la Sen

“…In this article, we introduce Reich type contractions and (α,F)-contractions in the class of controlled metric spaces and establish some new related fixed point theorems. …”
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On Asymptotic Pointwise Contractions in Modular Metric Spaces by Afrah A. N. Abdou

“…In this paper we study and prove some new fixed points theorems for pointwise and asymptotic pointwise contraction mappings in modular metric spaces.…”
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From homogeneous metric spaces to Lie groups by Cowling, Michael G., Kivioja, Ville, Le Donne, Enrico, Nicolussi Golo, Sebastiano, Ottazzi, Alessandro

“…We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively.After a review of a number of classical results, we use the Gleason–Iwasawa–Montgomery–Yamabe–Zippin structure theory to show that for all positive $ \epsilon $, each such space is $ (1,\epsilon ) $-quasi-isometric to a connected metric Lie group (metrized with a left-invariant distance that is not necessarily Riemannian).Next, we develop the structure theory of Lie groups to show that every homogeneous metric manifold is homeomorphically roughly isometric to a quotient space of a connected amenable Lie group, and roughly isometric to a simply connected solvable metric Lie group.Third, we investigate solvable metric Lie groups in more detail, and expound on and extend work of Gordon and Wilson [31, 32] and Jablonski [44] on these, showing, for instance, that connected solvable Lie groups may be made isometric if and only if they have the same real-shadow.Finally, we show that homogeneous metric spaces that admit a metric dilation are all metric Lie groups with an automorphic dilation.…”
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A metric space associated with probability space by Keith F. Taylor, Xikui Wang

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Quasi-Contractive Mappings in Modular Metric Spaces by Yeol J. E. Cho, Reza Saadati, Ghadir Sadeghi

“…We prove the existence of fixed point and uniqueness of quasi-contractive mappings in modular metric spaces which was introduced by Ćirić…”
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Precompactness and total boundedness in products of metric spaces by Bart Windels

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On π-Images of Locally Separable Metric Spaces by Tran Van An, Nguyen Van Dung

“…We characterize π-images of locally separable metric spaces by means of covers having π-property. As its application, we obtain characterizations of compact-covering (sequence-covering, pseudo-sequence-covering, and sequentially quotient) π-images of locally sparable metric spaces.…”
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On Orthogonal Partial b-Metric Spaces with an Application by Khalil Javed, Hassen Aydi, Fahim Uddin, Muhammad Arshad

“…In this paper, we initiate the concept of orthogonal partial b-metric spaces. We ensure the existence of a unique fixed point for some orthogonal contractive type mappings. …”
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