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Journal articles on the topic 'Partial Metric Spaces'

Author: Grafiati

Published: 18 May 2024

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1

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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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

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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Gregori, Valentín, Juan-José Miñana, and David Miravet. "Fuzzy partial metric spaces." International Journal of General Systems 48, no. 3 (December 2018): 260–79. http://dx.doi.org/10.1080/03081079.2018.1552687.

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5

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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6

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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7

Mykhaylyuk, Volodymyr, and Vadym Myronyk. "Metrizability of partial metric spaces." Topology and its Applications 308 (March 2022): 107949. http://dx.doi.org/10.1016/j.topol.2021.107949.

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8

Mukheimer, Aiman. "Extended Partial Sb-Metric Spaces." Axioms 7, no. 4 (November 21, 2018): 87. http://dx.doi.org/10.3390/axioms7040087.

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In this paper, we introduce the concept of extended partial S b -metric spaces, which is a generalization of the extended S b -metric spaces. Basically, in the triangle inequality, we add a control function with some very interesting properties. These new metric spaces generalize many results in the literature. Moreover, we prove some fixed point theorems under some different contractions, and some examples are given to illustrate our results.

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9

Yue, Yueli, and Meiqi Gu. "Fuzzy partial (pseudo-)metric spaces." Journal of Intelligent & Fuzzy Systems 27, no. 3 (2014): 1153–59. http://dx.doi.org/10.3233/ifs-131078.

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10

Ge, Xun, and Shou Lin. "Completions of partial metric spaces." Topology and its Applications 182 (March 2015): 16–23. http://dx.doi.org/10.1016/j.topol.2014.12.013.

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11

Otafudu, Oliver Olela, and Oscar Valero. "On Information Orders on Metric Spaces." Information 12, no. 10 (October 18, 2021): 427. http://dx.doi.org/10.3390/info12100427.

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Information orders play a central role in the mathematical foundations of Computer Science. Concretely, they are a suitable tool to describe processes in which the information increases successively in each step of the computation. In order to provide numerical quantifications of the amount of information in the aforementioned processes, S.G. Matthews introduced the notions of partial metric and Scott-like topology. The success of partial metrics is given mainly by two facts. On the one hand, they can induce the so-called specialization partial order, which is able to encode the existing order structure in many examples of spaces that arise in a natural way in Computer Science. On the other hand, their associated topology is Scott-like when the partial metric space is complete and, thus, it is able to describe the aforementioned increasing information processes in such a way that the supremum of the sequence always exists and captures the amount of information, measured by the partial metric; it also contains no information other than that which may be derived from the members of the sequence. R. Heckmann showed that the method to induce the partial order associated with a partial metric could be retrieved as a particular case of a celebrated method for generating partial orders through metrics and non-negative real-valued functions. Motivated by this fact, we explore this general method from an information orders theory viewpoint. Specifically, we show that such a method captures the essence of information orders in such a way that the function under consideration is able to quantify the amount of information and, in addition, its measurement can be used to distinguish maximal elements. Moreover, we show that this method for endowing a metric space with a partial order can also be applied to partial metric spaces in order to generate new partial orders different from the specialization one. Furthermore, we show that given a complete metric space and an inf-continuous function, the partially ordered set induced by this general method enjoys rich properties. Concretely, we will show not only its order-completeness but the directed-completeness and, in addition, that the topology induced by the metric is Scott-like. Therefore, such a mathematical structure could be used for developing metric-based tools for modeling increasing information processes in Computer Science. As a particular case of our new results, we retrieve, for a complete partial metric space, the above-explained celebrated fact about the Scott-like character of the associated topology and, in addition, that the induced partial ordered set is directed-complete and not only order-complete.

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12

Wu, Yaoqiang. "On strongly partial-quasi k-metric spaces." Filomat 37, no. 6 (2023): 1825–34. http://dx.doi.org/10.2298/fil2306825w.

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In this paper, we introduce the concepts of partial-quasi k-metric spaces and strongly partial- quasi k-metric spaces, and their relationship to k-metric spaces and partial-quasi metric spaces are studied. Furthermore, we obtain some results on fixed point theorems in strongly partial-quasi k-metric spaces.

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13

Shukla, Satish. "Partial Rectangular Metric Spaces and Fixed Point Theorems." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/756298.

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The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results.

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14

Wu, Yaoqiang. "On partial fuzzy k-(pseudo-)metric spaces." AIMS Mathematics 6, no. 11 (2021): 11642–54. http://dx.doi.org/10.3934/math.2021677.

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<abstract><p>In this paper, we introduce the concept of partial fuzzy k-(pseudo-)metric spaces, which is a generalization of fuzzy metric type spaces which introduced by Saadati. Also, we study some properties in partial fuzzy k-metric spaces and give some examples to support our results. Furthermore, we investigate the topological structures of partial fuzzy k-pseudo-metric spaces. Finally, we prove the existence of fixed points in these spaces.</p></abstract>

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15

Mohsenalhosseini, S. A. M., H. Mazaheri, M. A. Dehghan, and A. Zareh. "Fixed Point for Partial Metric Spaces." ISRN Applied Mathematics 2011 (July 6, 2011): 1–6. http://dx.doi.org/10.5402/2011/657868.

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We consider the partial metric on a set X, define ϵ-fixed point for maps, and obtain some sufficient and necessary conditions on that, also we obtain some sufficient and necessary theorems on ϵ-fixed point.

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16

Romaguera, Salvador, and Michel Schellekens. "Partial metric monoids and semivaluation spaces." Topology and its Applications 153, no. 5-6 (December 2005): 948–62. http://dx.doi.org/10.1016/j.topol.2005.01.023.

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17

Altun, Ishak, Ferhan Sola, and Hakan Simsek. "Generalized contractions on partial metric spaces." Topology and its Applications 157, no. 18 (December 2010): 2778–85. http://dx.doi.org/10.1016/j.topol.2010.08.017.

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18

Lu, Hanchuan, Heng Zhang, and Wei He. "Some Remarks on Partial Metric Spaces." Bulletin of the Malaysian Mathematical Sciences Society 43, no. 4 (November 6, 2019): 3065–81. http://dx.doi.org/10.1007/s40840-019-00854-1.

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19

Ge, Xun, and Shou Lin. "Some questions on partial metric spaces." Applied Mathematics-A Journal of Chinese Universities 35, no. 4 (October 2020): 392–98. http://dx.doi.org/10.1007/s11766-020-3569-z.

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20

Aydi, Hassen, Mujahid Abbas, and Calogero Vetro. "Partial Hausdorff metric and Nadlerʼs fixed point theorem on partial metric spaces." Topology and its Applications 159, no. 14 (September 2012): 3234–42. http://dx.doi.org/10.1016/j.topol.2012.06.012.

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21

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 the corresponding quasi-metric $q_p(x,y)=p(x,y)-p(x,x)$. Topological and metrical properties of partial metric spaces have been studied by many mathematicians. According to \cite{HWZ}, a quasi-metric space $(X,q)$ is called: {\it sequentially isosceles} if $\lim\limits_{n\to\infty}q(y,x_n)=q(y,x)$ for any $y\in X$ and every sequence of $x_n\in X$ that converges to $x\in X$; {\it sequentially equilateral} if a sequence of $y_n\in X$ converges to $x\in X$ while there exists a convergent to $x$ sequence of $x_n\in X$ with $\lim\limits_{n\to\infty}q(y_n,x_n)=0$; {\it sequentially symmetric} a sequence of $x_n\in X$ converges to $x\in X$ while $\lim\limits_{n\to\infty}q(x_n,x)=0$; {\it metric-like} if $\lim\limits_{n\to\infty}q(x_n,x)=0$ for every convergent to $x\in X$ sequence of $x_n\in X$. It was proved in \cite{HWZ} and \cite{Lu-2020} that: $(i)$ every sequentially equilateral quasi-metric space is sequentially symmetric; $(ii)$ every metric-like quasi-metric space is sequentially isosceles; $(iii)$ every metric-like and sequentially symmetric quasi-metric space is sequentially equilateral. A topological characterization of sequentially isosceles, sequentially equilateral, sequentially symmetric and metric-like quasi-metric spaces were obtained. Moreover, examples which show that there are no other connections between the indicated types of spaces, except for $(i)-(iii)$ even in the class of metrizable partial metric spaces have been constructed.

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22

BERINDE, VASILE, and MITROFAN CHOBAN. "Generalized distances and their associate metrics. Impact on fixed point theory." Creative Mathematics and Informatics 22, no. 1 (2013): 23–32. http://dx.doi.org/10.37193/cmi.2013.01.05.

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In the last years there is an abundance of fixed point theorems in literature, most of them established in various generalized metric spaces. Amongst the generalized spaces considered in those papers, we may find: cone metric spaces, quasimetric spaces (or b-metric spaces), partial metric spaces, G-metric spaces etc. In some recent papers [Haghi, R. H., Rezapour, Sh. and Shahzad, N., Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011), 1799-1803], [Haghi, R. H., Rezapour, Sh. and Shahzad, N., Be careful on partial metric fixed point results, Topology Appl., 160 (2013), 450-454], [Samet, B., Vetro, C. and Vetro, F., Remarks on G-Metric Spaces, Int. J. Anal., Volume 2013, Article ID 917158, 6 pages http://dx.doi.org/10.1155/2013/917158], the authors pointed out that some of the fixed point theorems transposed from metric spaces to cone metric spaces, partial metric spaces or G-metric spaces, respectively, are sometimes not real generalizations. The main aim of the present note is to inspect what happens in this respect with b-metric spaces.

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23

Ahmad, Haroon, Mudasir Younis, and Mehmet Emir Köksal. "Double Controlled Partial Metric Type Spaces and Convergence Results." Journal of Mathematics 2021 (December 14, 2021): 1–11. http://dx.doi.org/10.1155/2021/7008737.

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In this paper, we firstly propose the notion of double controlled partial metric type spaces, which is a generalization of controlled metric type spaces, partial metric spaces, and double controlled metric type spaces. Secondly, our aim is to study the existence of fixed points for Kannan type contractions in the context of double controlled partial metric type spaces. The proposed results enrich, theorize, and sharpen a multitude of pioneer results in the context of metric fixed point theory. Additionally, we provide numerical examples to illustrate the essence of our obtained theoretical results.

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24

ROMAGUERA, SALVADOR, and OSCAR VALERO. "A quantitative computational model for complete partial metric spaces via formal balls." Mathematical Structures in Computer Science 19, no. 3 (June 2009): 541–63. http://dx.doi.org/10.1017/s0960129509007671.

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Given a partial metric space (X, p), we use (BX, ⊑dp) to denote the poset of formal balls of the associated quasi-metric space (X, dp). We obtain characterisations of complete partial metric spaces and sup-separable complete partial metric spaces in terms of domain-theoretic properties of (BX, ⊑dp). In particular, we prove that a partial metric space (X, p) is complete if and only if the poset (BX, ⊑dp) is a domain. Furthermore, for any complete partial metric space (X, p), we construct a Smyth complete quasi-metric q on BX that extends the quasi-metric dp such that both the Scott topology and the partial order ⊑dp are induced by q. This is done using the partial quasi-metric concept recently introduced and discussed by H. P. Künzi, H. Pajoohesh and M. P. Schellekens (Künzi et al. 2006). Our approach, which is inspired by methods due to A. Edalat and R. Heckmann (Edalat and Heckmann 1998), generalises to partial metric spaces the constructions given by R. Heckmann (Heckmann 1999) and J. J. M. M. Rutten (Rutten 1998) for metric spaces.

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25

Kanwal, Tanzeela, Azhar Hussain, Poom Kumam, and Ekrem Savas. "Weak Partial b-Metric Spaces and Nadler’s Theorem." Mathematics 7, no. 4 (April 5, 2019): 332. http://dx.doi.org/10.3390/math7040332.

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The purpose of this paper is to define the notions of weak partial b-metric spaces and weak partial Hausdorff b-metric spaces along with the topology of weak partial b-metric space. Moreover, we present a generalization of Nadler’s theorem by using weak partial Hausdorff b-metric spaces in the context of a weak partial b-metric space. We present a non-trivial example which show the validity of our result and an application to nonlinear Volterra integral inclusion for the applicability purpose.

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26

Schellekens, M. P. "Extendible spaces." Applied General Topology 3, no. 2 (October 1, 2002): 169. http://dx.doi.org/10.4995/agt.2002.2061.

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<p>The domain theoretic notion of lifting allows one to extend a partial order in a trivial way by a minimum. In the context of Quantitative Domain Theory partial orders are represented as quasi-metric spaces. For such spaces, the notion of the extension by an extremal element turns out to be non trivial.</p><p>To some extent motivated by these considerations, we characterize the directed quasi-metric spaces extendible by an extremum. The class is shown to include the S-completable directef quasi-metric spaces. As an application of this result, we show that for the case of the invariant quasi-metric (semi)lattices, weightedness can be characterized by order convexity with the extension property.</p>

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27

Ansar, Ahmad, and Syamsuddin Mas'ud. "Fixed point results in α, β partial b-metric spaces using C-contraction type mapping and its generalization." Journal of Natural Sciences and Mathematics Research 8, no. 2 (December 31, 2022): 111–19. http://dx.doi.org/10.21580/jnsmr.2022.8.2.12778.

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Banach contraction mapping has main role in nonlinear analysis courses and has been modified to get new kind of generalizations in some abstract spaces to produce many fixed point theory. Fixed point theory has been proved in partial metric spaces and b-metric spaces as generalizations of metric spaces to obtain new theorems. In addition, using modified of contraction mapping we get some fixed point that have been used to solve differential equations or integral equations, and have many applications. Therefore, this area is actively studied by many researchers. The goal of this article is present and prove some fixed point theorems for extension of contraction mapping in α, β partial b-metric spaces. In this research, we learn about notions of b-metric spaces and partial metric that are combined to generated partial b-metric spaces from many literatures. Afterwards, generalizations are made to get α, β partial b-metric spaces. Using the properties of convergence, Cauchy sequences, and notions of completeness in α, β partial b-metric spaces, we prove some fixed point theorem. Fixed point theory that we generated used C-contraction mapping and its generalizations with some conditions. Existence and uniqueness of fixed point raised for some restrictions of α, β conditions. Some corollaries of main results are also proved. Our main theorems extend and increase some existence in the previous results.©2022 JNSMR UIN Walisongo. All rights reserved.

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28

Huang, Xianjiu, Chuanxi Zhu, and Xi Wen. "Fixed point theorems for expanding mappings in partial metric spaces." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 1 (May 1, 2012): 213–24. http://dx.doi.org/10.2478/v10309-012-0014-7.

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AbstractIn this paper, we define expanding mappings in the setting of partial metric spaces analogous to expanding mappings in metric spaces. We also obtain some results for two mappings to the setting of partial metric spaces

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29

Simkhah, Asil, Shaban Sedghi, and Zoran Mitrovic. "Partial S-metric spaces and coincidence points." Filomat 33, no. 14 (2019): 4613–26. http://dx.doi.org/10.2298/fil1914613s.

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In this paper, the concept partial S-metric space is introduced as a generalization of S-metric space. We prove certain coincidence point theorems in partial S-metric spaces. The results we obtain generalize many known results in fixed point theory. Also, some examples show the e_ectiveness of this approach.

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30

Alsamir, Habes, Mohd Noorani, Wasfi Shatanawi, and Kamal Abodyah. "Common fixed point results for generalized (ψ,β)-geraghty contraction type mapping in partially ordered metric-like spaces with application." Filomat 31, no. 17 (2017): 5497–509. http://dx.doi.org/10.2298/fil1717497a.

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Harandi [A. A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages] introduced the notion of metric-like spaces as a generalization of partial metric spaces and studied some fixed point theorems in the context of the metric-like spaces. In this paper, we utilize the notion of the metric-like spaces to introduce and prove some common fixed points theorems for mappings satisfying nonlinear contractive conditions in partially ordered metric-like spaces. Also, we introduce an example and an application to support our work. Our results extend and modify some recent results in the literature.

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31

Souayah, Nizar. "A Fixed Point in Partial Sb-Metric Spaces." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 3 (November 1, 2016): 351–62. http://dx.doi.org/10.1515/auom-2016-0062.

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AbstractIn this paper, we introduce an interesting extention of the partial b-metric spaces called partial Sb-metric spaces, and we show the existence of fixed point for a self mapping defined on such spaces.

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32

Sila, Eriola, Sidite Duraj, and Elida Hoxha. "Some Fixed Point Results in Partial Rectangular Metric-Like Spaces." Journal of Mathematics 2021 (October 20, 2021): 1–9. http://dx.doi.org/10.1155/2021/5577776.

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In this paper, we introduce a new concept of partial rectangular metric-like space and prove some results on the existence and uniqueness of a fixed point of a function T : X ⟶ X , defined on a partial rectangular metric-like space X , which fulfills a nonlinear contractive condition using a comparison function and the diameter of the orbits. The obtained results generalize some previously acknowledged results in partial metric spaces, partial rectangular metric spaces, and rectangular metric-like spaces. The examples presented prove the usefulness of the introduced generalizations.

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33

Ozturk, Vildan. "Integral Type F-Contractions in Partial Metric Spaces." Journal of Function Spaces 2019 (March 25, 2019): 1–8. http://dx.doi.org/10.1155/2019/5193862.

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Partial metric spaces were introduced as a generalization of usual metric spaces where the self-distance for any point need not be equal to zero. In this work, we defined generalized integral type F-contractions and proved common fixed point theorems for four mappings satisfying this type (Branciari type) of contractions in partial metric spaces.

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34

Ðukić, Dušan, Zoran Kadelburg, and Stojan Radenović. "Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces." Abstract and Applied Analysis 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/561245.

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Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

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35

Shukla, Satish, Ishak Altun, and Ravindra Sen. "Fixed Point Theorems and Asymptotically Regular Mappings in Partial Metric Spaces." ISRN Computational Mathematics 2013 (May 23, 2013): 1–6. http://dx.doi.org/10.1155/2013/602579.

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The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are also proved which generalize and improve some known results in partial metric spaces.

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36

Agarwal, Ravi P., Mohamed Jleli, and Bessem Samet. "Some Integral Inequalities Involving Metrics." Entropy 23, no. 7 (July 8, 2021): 871. http://dx.doi.org/10.3390/e23070871.

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In this work, we establish some integral inequalities involving metrics. Moreover, some applications to partial metric spaces are given. Our results are extension of previous obtained metric inequalities in the discrete case.

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37

Aydi, Hassen, Samina Batul, Muhammad Aslam, Dur-e.-Shehwar Sagheer, and Eskandar Ameer. "Fixed Point Results for Single and Multivalued Maps on Partial Extended b -Metric Spaces." Journal of Function Spaces 2022 (May 23, 2022): 1–8. http://dx.doi.org/10.1155/2022/2617972.

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This article is based on the concept of partial extended b -metric spaces, which is inspired by the notions of new extended b -metric spaces and partial metric spaces. Fixed point results for single and multivalued mappings on such spaces are also presented. Few examples are also provided to elaborate the concepts.

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38

Bugajewski, Dariusz, and Ruidong Wang. "On the topology of partial metric spaces." Mathematica Slovaca 70, no. 1 (February 25, 2020): 135–46. http://dx.doi.org/10.1515/ms-2017-0338.

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AbstractIn this paper, we give some necessary and sufficient conditions under which the topology generated by a partial metric is equivalent to the topology generated by a suitably defined metric. Next, we study some new extensions of the Generalized Banach Contraction Principle to partial metric spaces. Moreover, we draw a particular attention to the space of all sequences showing, in particular, that some well-known fixed point theorems for ultrametric spaces, can be used for operators acting in that space. We illustrate our considerations by suitable examples and counterexamples.

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39

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 metric-like space and also for the complex distance between two subsets of a complex valued metric-like space. In addition, the topological properties of this space are also investigated.

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40

Ayoob, Irshad, Ng Zhen Chuan, and Nabil Mlaiki. "Double-Controlled Quasi M-Metric Spaces." Symmetry 15, no. 4 (April 10, 2023): 893. http://dx.doi.org/10.3390/sym15040893.

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One of the well-studied generalizations of a metric space is known as a partial metric space. The partial metric space was further generalized to the so-called M-metric space. In this paper, we introduce the Double-Controlled Quasi M-metric space as a new generalization of the M-metric space. In our new generalization of the M-metric space, the symmetry condition is not necessarily satisfied and the triangle inequality is controlled by two binary functions. We establish some fixed point results, along with the examples and applications to illustrate our results.

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41

Dung, Nguyen Van. "On the completion of partial metric spaces." Quaestiones Mathematicae 40, no. 5 (April 11, 2017): 589–97. http://dx.doi.org/10.2989/16073606.2017.1303004.

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42

Krishnakumar, R., and R. Livingston. "Fixed Point Theorem in Partial Metric Spaces." International Journal of Scientific Research in Mathematical and Statistical Sciences 5, no. 4 (August 31, 2018): 384–88. http://dx.doi.org/10.26438/ijsrmss/v5i4.384388.

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43

Van, Dung, and Hang Le. "A note on partial rectangular metric spaces." Mathematica Moravica 18, no. 1 (2014): 1–8. http://dx.doi.org/10.5937/matmor1401001v.

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44

Conant, Gabriel. "Extending partial isometries of generalized metric spaces." Fundamenta Mathematicae 244, no. 1 (2019): 1–16. http://dx.doi.org/10.4064/fm484-9-2018.

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45

Han, Suzhen, Jianfeng Wu, and Dong Zhang. "Properties and principles on partial metric spaces." Topology and its Applications 230 (October 2017): 77–98. http://dx.doi.org/10.1016/j.topol.2017.08.006.

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46

Mykhaylyuk, Volodymyr, and Vadym Myronyk. "Compactness and completeness in partial metric spaces." Topology and its Applications 270 (February 2020): 106925. http://dx.doi.org/10.1016/j.topol.2019.106925.

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47

Saxena, Swati, and U. C. Gairola. "HYBRID CONTRACTION IN WEAK PARTIAL METRIC SPACES." jnanabha 52, no. 02 (2022): 228–36. http://dx.doi.org/10.58250/jnanabha.2022.52227.

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48

Ge, Xun, and Shou Lin. "A Note on Partial b-Metric Spaces." Mediterranean Journal of Mathematics 13, no. 3 (March 3, 2015): 1273–76. http://dx.doi.org/10.1007/s00009-015-0548-9.

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49

Ilchev, Atanas, and Diana Nedelcheva-Arnaudova. "Coupled Fixed Points in Partial Metric Spaces." Geometry, Integrability and Quantization 26 (2023): 27–38. http://dx.doi.org/10.7546/giq-26-2023-27-38.

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50

Al Rwaily, Asma, and A. M. Zidan. "New Contributions in Generalization S -Metric Spaces to S ∗ p -Partial Metric Spaces with Some Results in Common Fixed Point Theorems." Complexity 2021 (May 19, 2021): 1–8. http://dx.doi.org/10.1155/2021/5584685.

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Abstract:

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. Also, we give some of the topological properties that are important in knowing the convergence of the sequences and Cauchy sequence. Finally, we study a new common fixed point theorems in this spaces.

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