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Journal articles on the topic 'Rectangular S metric spaces'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Asmita, Yadav, and S. Saluja A. "A Result on Fixed Points in Rectangular S-Metric Spaces." International Journal of Mathematics and Computer Research 13, no. 05 (2025): 5190–92. https://doi.org/10.5281/zenodo.15432783.

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In this paper, the notion of rectangular S-metric which extends rectangular metric spaces introduced by Branciari. The results obtained expand and generalize several well-established findings in the existing literature. <strong>MATHEMATICS SUBJECT CLASSIFICATION (2020) :</strong> Primary: 54H25; Secondary:54E50, 47H10.

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2

Haque, Salma, Fatima Azmi, and Nabil Mlaiki. "Fredholm Type Integral Equation in Controlled Rectangular Metric-like Spaces." Symmetry 14, no. 5 (2022): 991. http://dx.doi.org/10.3390/sym14050991.

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In this article, we present an extension of the controlled rectangular b-metric spaces, so-called controlled rectangular metric-like spaces, where we keep the symmetry condition and we only change the condition [D(s,r)=0⇔s=r]to[D(s,r)=0⇒s=r], which means we may have a non-zero self distance; also, D(s,s) is not necessarily less than D(s,r). This new type of metric space is a generalization of controlled rectangular b-metric spaces and partial rectangular metric spaces.

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3

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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4

Gautam, Pragati, Luis Manuel Sánchez Ruiz, and Swapnil Verma. "Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space." Symmetry 13, no. 1 (2020): 32. http://dx.doi.org/10.3390/sym13010032.

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The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

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Furqan, Salman, Hüseyin Işık, and Naeem Saleem. "Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results." Journal of Function Spaces 2021 (May 20, 2021): 1–8. http://dx.doi.org/10.1155/2021/9936992.

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In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b -metric space, fuzzy b -metric space, and extended fuzzy b -metric space. We use f , g , h , three noncomparable functions as follows: m q μ , η , t + s + w ≥ m q μ , ν , t / f μ , ν ∗ m q ν , ξ , s / g ν , ξ ∗ m q ξ , η , w / h ξ , η . We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. An example is presented to suppo

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Zubair, Sumaiya Tasneem, Kalpana Gopalan, Thabet Abdeljawad, and Bahaaeldin Abdalla. "On Fuzzy Extended Hexagonal b-Metric Spaces with Applications to Nonlinear Fractional Differential Equations." Symmetry 13, no. 11 (2021): 2032. http://dx.doi.org/10.3390/sym13112032.

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The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal b-metric spaces is specified as follows utilizing the function b(c,d): mhc,d,t+s+u+v+w≥mhc,e,tb(c,d)∗mhe,f,sb(c,d)∗mhf,g,ub(c,d)∗mhg,k,vb(c,d)∗mhk,d,wb(c,d) for all t,s,u,v,w>0 and c≠e,e

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7

Hussain, Aftab, Hamed Al Sulami, and Umar Ishtiaq. "Some New Aspects in the Intuitionistic Fuzzy and Neutrosophic Fixed Point Theory." Journal of Function Spaces 2022 (March 3, 2022): 1–14. http://dx.doi.org/10.1155/2022/3138740.

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In this manuscript, we use the concepts of continuous t-norms and continuous t-conorms to introduce some definitions, in which intuitionistic fuzzy rectangular metric spaces, intuitionistic fuzzy rectangular metric-like spaces, intuitionistic fuzzy rectangular b-metric spaces, intuitionistic fuzzy rectangular b-metric-like spaces, neutrosophic rectangular metric spaces, neutrosophic rectangular metric-like spaces, neutrosophic rectangular b-metric spaces, and neutrosophic rectangular b-metric-like spaces are included. Continuous t-norms and continuous t-conorms are used to generalize the proba

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Hussain, Nawab, Nawal Alharbi, and Ghada Basendwah. "Fixed-Point Results with Applications in Generalized Neutrosophic Rectangular b-Metric Spaces." Axioms 13, no. 12 (2024): 818. http://dx.doi.org/10.3390/axioms13120818.

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In this paper, we introduce several new concepts: generalized neutrosophic rectangular b-metric-like spaces (GNRBMLSs), generalized intuitionistic rectangular b-metric-like spaces (GIRBMLSs), and generalized fuzzy rectangular b-metric-like spaces (GFRBMLSs). These innovative spaces can expand various topological spaces, including neutrosophic rectangular extended b-metric-like spaces, intuitionistic fuzzy rectangular extended b-metric-like spaces, and fuzzy rectangular extended b-metric-like spaces. Moreover, we establish Banach’s fixed point theorem and Ćirić’s quasi-contraction theorem with

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9

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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10

Rossafi, Mohamed, та Kari Abdelkarim. "Fixed point theorems for generalized θ-φ-contraction mappings in rectangular quasi b-metric spaces". Annals of Mathematics and Computer Science 27 (23 березня 2025): 1–16. https://doi.org/10.56947/amcs.v27.473.

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A generalized version of both rectangular metric spaces and rectangular quasi-metric spaces is known as rectangular quasi b-metric spaces (RQB-MS). In the current work, we define generalized ( θ,φ)-contraction mappings and study fixed point (FP) results for the maps introduced in the setting of rectangular quasi b-metric spaces. Our results generalize many existing results. We also provide examples in support of our main findings.

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11

Younis, Mudasir, Nicola Fabiano, Zaid Fadail, Zoran Mitrović, and Stojan Radenović. "Some new observations on fixed point results in rectangular metric spaces with applications to chemical sciences." Vojnotehnicki glasnik 69, no. 1 (2021): 8–30. http://dx.doi.org/10.5937/vojtehg69-29517.

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Introduction/purpose: This paper considers, generalizes and improves recent results on fixed points in rectangular metric spaces. The aim of this paper is to provide much simpler and shorter proofs of some new results in rectangular metric spaces. Methods: Some standard methods from the fixed point theory in generalized metric spaces are used. Results: The obtained results improve the well-known results in the literature. The new approach has proved that the Picard sequence is Cauchy in rectangular metric spaces. The obtained results are used to prove the existence of solutions to some nonline

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Malhotra, S. K., J. B. Sharma, and Satish Shukla. "g-Weak Contraction in Ordered Cone Rectangular Metric Spaces." Scientific World Journal 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/810732.

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We prove some common fixed-point theorems for the orderedg-weak contractions in cone rectangular metric spaces without assuming the normality of cone. Our results generalize some recent results from cone metric and cone rectangular metric spaces into ordered cone rectangular metric spaces. Examples are provided which illustrate the results.

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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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14

Kattan, Doha, Amjad Owaidh Alzanbaqi, and Sahidul Islam. "Contraction Mappings in Intuitionistic Fuzzy Rectangular Extended B-Metric Spaces." Mathematical Problems in Engineering 2022 (April 23, 2022): 1–21. http://dx.doi.org/10.1155/2022/1814291.

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In this study, we present the notion of intuitionistic fuzzy rectangular extended b-metric spaces as a generalization of intuitionistic fuzzy metric spaces and intuitionistic fuzzy rectangular b-metric spaces. Some well-known fixed-point results in metric fixed-point theory are generalized in the sense of intuitionistic fuzzy rectangular extended b-metric spaces. Several nontrivial examples and an application to nonlinear fractional differential equations are also imparted in this work to examine the validity of given results.

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15

Li, Chaobo, Yunan Cui, and Lili Chen. "Fixed Point Results on Closed Ball in Convex Rectangular b − Metric Spaces and Applications." Journal of Function Spaces 2022 (April 28, 2022): 1–13. http://dx.doi.org/10.1155/2022/8840964.

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In this paper, the concept of convex rectangular b − metric spaces is introduced as a generalization of both convex metric spaces and rectangular b − metric spaces. The purpose of this study is to indicate a way of generalizing Mann’s iteration algorithm and a series of fixed point results in rectangular b − metric spaces. Furthermore, certain examples are given to support the results. We also study well posedness of fixed point problems of some mappings in convex rectangular b − metric spaces, and an application to the dynamic programming is entrusted to manifest the viability of the obtained

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16

Alamgir, Nayab, Quanita Kiran, Hassen Aydi, and Yaé Ulrich Gaba. "On Controlled Rectangular Metric Spaces and an Application." Journal of Function Spaces 2021 (April 30, 2021): 1–9. http://dx.doi.org/10.1155/2021/5564324.

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In this paper, we introduce the notion of controlled rectangular metric spaces as a generalization of rectangular metric spaces and rectangular b -metric spaces. Further, we establish some related fixed point results. Our main results extend many existing ones in the literature. The obtained results are also illustrated with the help of an example. In the last section, we apply our results to a common real-life problem in a general form by getting a solution for the Fredholm integral equation in the setting of controlled rectangular metric spaces.

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17

Adewale, O. K., J. O. Olaleru, H. Olaoluwa, and H. Akewe. "Fixed Point Theorems on Generalized Rectangular Metric Spaces." Journal of Mathematical Sciences: Advances and Applications 65, no. 1 (2021): 59–84. http://dx.doi.org/10.18642/jmsaa_7100122185.

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In this paper, we introduce the notion of generalized rectangular metric spaces which extends rectangular metric spaces introduced by Branciari. Analogues of the some well-known fixed point theorems are proved in this space. With an example, it is shown that a generalized rectangular metric space is neither a G-metric space nor a rectangular metric space. Our results generalize many known results in fixed point theory.

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18

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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19

Saleem, Naeem, Salman Furqan, and Fahd Jarad. "On Extended b -Rectangular and Controlled Rectangular Fuzzy Metric-Like Spaces with Application." Journal of Function Spaces 2022 (July 18, 2022): 1–14. http://dx.doi.org/10.1155/2022/5614158.

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In this article, we introduce the notions of extended b -rectangular and controlled rectangular fuzzy metric-like spaces that generalize many fuzzy metric spaces in the literature. We give examples to justify our newly defined fuzzy metric-like spaces and prove that these spaces are not Hausdorff. We use fuzzy contraction and prove Banach fixed point theorems in these spaces. As an application, we utilize our main results to solve the uniqueness of the solution of a differential equation occurring in the dynamic market equilibrium.

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20

Özgür, Nihal Yılmaz, Nabil Mlaiki, Nihal Taş, and Nizar Souayah. "A new generalization of metric spaces: rectangular M-metric spaces." Mathematical Sciences 12, no. 3 (2018): 223–33. http://dx.doi.org/10.1007/s40096-018-0262-4.

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21

Mustafa, Zead, Vahid Parvaneh, Mohammed M. M. Jaradat, and Zoran Kadelburg. "Extended Rectangular b-Metric Spaces and Some Fixed Point Theorems for Contractive Mappings." Symmetry 11, no. 4 (2019): 594. http://dx.doi.org/10.3390/sym11040594.

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In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate these results.

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22

Tiwari, Jayesh, and Dileep Kumar Sharma. "EXISTENCE AND UNIQUENESS OF FIXED POINT FOR NEW CONTRACTIONS IN RECTANGULAR b-METRIC SPACES." South East Asian J. of Mathematics and Mathematical Sciences 18, no. 03 (2022): 139–52. http://dx.doi.org/10.56827/seajmms.2022.1803.11.

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In this article, we give some new examples of rectangular b-metric spaces which are neither rectangular metric space nor metric space. After that we prove existence and uniqueness of new fixed points for some new contractions in rectangular b-metric spaces. Then we validate these results with suitable, appro- priate and innovative examples.

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23

Li, Chaobo, and Yunan Cui. "Rectangular Gb-Metric Spaces and Some Fixed Point Theorems." Axioms 11, no. 3 (2022): 108. http://dx.doi.org/10.3390/axioms11030108.

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In this paper, we first introduce the concept of rectangular Gb-metric space which generalizes the notion of rectangular metric space and Gb-metric space. Then, some fixed point results connected with certain contractions are obtained in the setting of rectangular Gb-metric spaces. Additionally, we also introduce the concept of convex rectangular Gb-metric space by means of the convex structure and study the fixed points of enriched type contractions in this space.

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Formica, Maria Rosaria, and Abdelkarim Kari. "New Fixed Point Theorems in Complete Rectangular M-metric Spaces." WSEAS TRANSACTIONS ON MATHEMATICS 23 (December 12, 2024): 863–73. https://doi.org/10.37394/23206.2024.23.89.

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In this article we extend the Banach contraction principle known in the framework of rectangular metric spaces (θ-contraction) to the more general rectangular M-metric spaces. We also investigate the existence and uniqueness of fixed point for mappings satisfying θ-contraction in rectangular M-metric spaces. Moreover, we provide some examples to highlight the obtained improvements. Finally, as an application, we investigate the existence and uniqueness of a solution of a non-linear integral equation of Fredholm type.

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Aydi, Hassen, Nihal Taş, Nihal Özgür, and Nabil Mlaiki. "Fixed-Discs in Rectangular Metric Spaces." Symmetry 11, no. 2 (2019): 294. http://dx.doi.org/10.3390/sym11020294.

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In this manuscript, we present some results related to fixed-discs of self-mappings in rectangular metric spaces. To do this, we give new techniques modifying some classical notions such as Banach contraction principle, α-admissible mappings and Brianciari type contractions. We give necessary illustrative examples to show the validity of our obtained theoretical theorems. Our results are generalizations of some fixed-circle results existing in the literature.

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Azam, Akbar, Muhammad Arshad, and Ismat Beg. "Banach contraction principle on cone rectangular metric spaces." Applicable Analysis and Discrete Mathematics 3, no. 2 (2009): 236–41. http://dx.doi.org/10.2298/aadm0902236a.

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Asim, Nisar, Morsy, and Imdad. "Extended Rectangular Mrc-Metric Spaces and Fixed Point Results." Mathematics 7, no. 12 (2019): 1136. http://dx.doi.org/10.3390/math7121136.

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In this paper, we enlarge the classes of rectangular Mb-metric spaces and extendedrectangular b-metric spaces by considering the class of extended rectangular Mrc-metric spacesand utilize the same to prove an analogue of Banach contraction principle in such spaces. We adoptan example to highlight the utility of our main result. Finally, we apply our result to examine theexistence and uniqueness of solution for a system of Fredholm integral equation.

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28

Saleem, Naeem, Salman Furqan, Kinda Abuasbeh, and Muath Awadalla. "Fuzzy Triple Controlled Metric like Spaces with Applications." Mathematics 11, no. 6 (2023): 1390. http://dx.doi.org/10.3390/math11061390.

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In this article, we introduce the concept of a fuzzy triple controlled metric like space in the sense that the self distance may not be equal to one. We have used three functions in our space that generalize fuzzy controlled rectangular, extended fuzzy rectangular, fuzzy b–rectangular and fuzzy rectangular metric like spaces. Various examples are given to justify our definitions and results. As for the topological aspect, we prove a fuzzy triple controlled metric like space is not Hausdorff. We also apply our main result to solve the uniqueness of the solution of a fractional differential equa

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Ishtiaq, Umar, Aftab Hussain, and Hamed Al Sulami. "Certain new aspects in fuzzy fixed point theory." AIMS Mathematics 7, no. 5 (2022): 8558–73. http://dx.doi.org/10.3934/math.2022477.

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<abstract> <p>We will establish several fixed point results in new introduced spaces in this manuscript known as fuzzy rectangular metric-like spaces and rectangular b-metric-like spaces. These new results and spaces will improve the approach of existing ones in the literature. Few non-trivial examples and an application also verify the uniqueness of solution.</p> </abstract>

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30

Srivastava, M., and S. C. Ghosh. "Cone Metric Spaces, Cone Rectangular Metric Spaces and Common Fixed Point Theorems." International Journal of Mathematics Trends and Technology 47, no. 1 (2017): 5–13. http://dx.doi.org/10.14445/22315373/ijmtt-v47p502.

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31

Ghasab, Ehsan Lotfali, Reza Chaharpashlou, and António M. Lopes. "Solving a System of Integral Equations in Rectangular Menger Probabilistic Metric Spaces and Rectangular Menger Probabilistic b-Metric Spaces." Symmetry 15, no. 1 (2022): 70. http://dx.doi.org/10.3390/sym15010070.

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This work introduces the concepts of rectangular Menger probabilistic metric (RMPM) space and rectangular Menger probabilistic b-metric (RMPbM) space as generalizations of the Menger probabilistic metric space and the Menger probabilistic b-metric space, respectively. Some nonunique fixed-point and coupled-fixed-point results for contractive mappings are provided. The findings extend and improve outcomes presented in the existing literature. The main results are illustrated with examples, and validated by means of an application to a system of integral equations. The importance of spaces with

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Alamgir, N., Q. Kiran, Y. Ali, and H. Aydi. "Some fixed point results on controlled rectangular partial metric spaces with a graph structure." Carpathian Mathematical Publications 17, no. 1 (2025): 343–63. https://doi.org/10.15330/cmp.17.1.343-363.

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In this work, we define a controlled rectangular partial metric space, which is a generalization of a controlled rectangular metric space and a controlled metric space. Furthermore, we derive some fixed point results with suitable conditions in this setting. As an application, we give a fixed point theorem for graphic contractions on a controlled rectangular partial metric space via a graph structure.

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33

Azmi, Fatima M. "Exploring Fuzzy Triple Controlled Metric Spaces: Applications in Integral Equations." Symmetry 15, no. 10 (2023): 1943. http://dx.doi.org/10.3390/sym15101943.

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In this article, we delve into the study of fuzzy triple controlled metric spaces, investigating their properties and presenting a range of illustrative examples. We emphasize the broader applicability of this concept in comparison to fuzzy rectangular metric spaces and fuzzy rectangular b-metric spaces. By introducing the novel concept of (α-ψ)-fuzzy contractive mappings, we derive fixed point results specifically designed for complete fuzzy triple controlled metric spaces. Our theorems extend and enrich previous findings in this field. Additionally, we demonstrate the practical significance

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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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Dung, Nguyen Van. "The metrization of rectangular b-metric spaces." Topology and its Applications 261 (July 2019): 22–28. http://dx.doi.org/10.1016/j.topol.2019.04.010.

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Ding, Hui-Sheng, Mohammad Imdad, Stojan Radenović, and Jelena Vujaković. "On some fixed point results in b-metric, rectangular and b-rectangular metric spaces." Arab Journal of Mathematical Sciences 22, no. 2 (2016): 151–64. http://dx.doi.org/10.1016/j.ajmsc.2015.05.003.

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Mlaiki, N., K. Abodayeh, H. Aydi, T. Abdeljawad, and M. Abuloha. "Rectangular Metric-Like Type Spaces and Related Fixed Points." Journal of Mathematics 2018 (September 3, 2018): 1–7. http://dx.doi.org/10.1155/2018/3581768.

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In this paper, we introduce the concept of a rectangular metric-like space, along with its topology, and we prove some fixed point theorems for different contraction types. We also introduce the concept of modified metric-like spaces and we prove some topological and convergence properties under the symmetric convergence. Some examples are given to illustrate the new introduced metric type spaces.

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38

Abbas, Mujahid, Vladimir Rakočević, and Zahra Noor. "Perov multivalued contraction pair in rectangular cone metric spaces." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 8, no. 3 (2021): 484–501. http://dx.doi.org/10.21638/spbu01.2021.310.

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Perov studied the Banach contraction principle in the framework of a generalized metric space and presented Perov contraction condition where the contractive constant is replaced by a matrix with nonnegative entries and spectral radius less than 1. Azam et al. presented the notion of rectangular cone metric space following the idea of Branciari, Huang and Zhang by replacing the triangular inequality in the cone metric space by rectangular inequality. Motivated by the work of Abbas and Vetro and Radenovi´c, the purpose of this paper is to introduce a new class of Perov type multivalued mappings

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Zheng, Dingwei, Guofei Ye, and Dawei Liu. "Sehgal–Guseman-Type Fixed Point Theorem in b-Rectangular Metric Spaces." Mathematics 9, no. 24 (2021): 3149. http://dx.doi.org/10.3390/math9243149.

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In this paper, we prove a Sehgal–Guseman-type fixed point theorem in b-rectangular metric spaces which provides a complete solution to an open problem raised by Zoran D. Mitrović (A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space). The result presented in the paper generalizes and unifies some results in fixed point theory.

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Aydi, Hassen, Zoran D. Mitrović, Stojan Radenović, and Manuel de la Sen. "On a Common Jungck Type Fixed Point Result in Extended Rectangular b-Metric Spaces." Axioms 9, no. 1 (2019): 4. http://dx.doi.org/10.3390/axioms9010004.

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In this paper, we present a Jungck type common fixed point result in extended rectangular b-metric spaces. We also give some examples and a known common fixed point theorem in extended b-metric spaces.

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Saleem, Naeem, Salman Furqan, Hossam A. Nabwey, and Reny George. "Survivability of AIDS Patients via Fractional Differential Equations with Fuzzy Rectangular and Fuzzy b-Rectangular Metric like Spaces." Symmetry 14, no. 11 (2022): 2450. http://dx.doi.org/10.3390/sym14112450.

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As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be regarded as the main advantage of this paper. In these spaces, the symmetry property is preserved, but the self distance may not be equal to one. We discuss topological properties and demonstrate that neither of these spaces is Hausdorff. Using α−ψ-contraction and Geraghty contractions, respectively, in our main results, we establish fixed p

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Pagidi, Mallikarjun Reddy. "A Common Fixed Point Theorem in Cone Rectangular Metric Space Under Expansive Type Condition." Indian Journal of Science and Technology 16, no. 32 (2023): 2510–17. https://doi.org/10.17485/IJST/v16i32.1303.

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Abstract <strong>Objectives:</strong> In this paper, we have to establish a generalized common fixed point theorem in cone rectangular metric spaces. <strong>Methods:</strong> In this paper, we use the Banach contraction principle technique to establish the generalized fixed point theorem. <strong>Findings:</strong> The paper presents a unique common fixed point theorem for two weakly compatible self-maps satisfying expansive type mapping in cone rectangular metric space without assuming the normality condition of a cone. Our result extends and supplements some well-kn

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Kumar, Krishan, Mamta Kamra, and Rajpal . "Common Fixed Point Results For Quadruple Transformations In Vector Valued Rectangular Metric Spaces." International Journal of Membrane Science and Technology 10, no. 4 (2023): 2488–99. http://dx.doi.org/10.15379/ijmst.v10i4.3605.

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In this manuscript, we consider vector valued Rectangular metric space in which metric is Riesz space valued. We establish the existence of common fixed point results for four self-maps in vector valued rectangular metric space. Established results extend and generalize several fixed point results for scalar valued case in the literature.

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44

Mitrović, Zoran D. "A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space." Mathematica Slovaca 68, no. 5 (2018): 1113–16. http://dx.doi.org/10.1515/ms-2017-0172.

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Abstract In this note we give very short proofs for Banach contraction principle theorem in the b-rectangular metric spaces and b-metric spaces. Our result provides a complete solution to an open problem raised by George, Radenović, Reshma and Shukla.

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Younis, Mudasir, Aleksandra Stretenović, and Stojan Radenović. "Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”." Nonlinear Analysis: Modelling and Control 27, no. 1 (2022): 163–78. http://dx.doi.org/10.15388/namc.2022.27.25193.

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In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve

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Pooja, Chaubey* &. Shishir Jain. "A REVIEW ON ABSTRACT SPACES AND FIXED POINT THEOREM." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES [FRTSSDS-18] (June 13, 2018): 65–68. https://doi.org/10.5281/zenodo.1288428.

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We discuss a brief introduction of cone metric space where the set of real number is replaced by real Banach space , partial rectangular metric space, partial--metric space etc. In each of these space several changes have been made or added in the properties of metric space which generalized the famous Banach contration principle.

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Kumar, Parveen, Savita Malik, and Manoj Kumar. "Stochastic Fixed Point Theorems in Rectangular Metric Spaces." Turkish Journal of Analysis and Number Theory 9, no. 1 (2021): 9–16. http://dx.doi.org/10.12691/tjant-9-1-2.

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Zheng, Dingwei, Pei Wang, and Nada Citakovic. "Meir-Keeler theorem in b-rectangular metric spaces." Journal of Nonlinear Sciences and Applications 10, no. 04 (2017): 1786–90. http://dx.doi.org/10.22436/jnsa.010.04.39.

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Sarita, Devi, and Pankaj Pankaj. "Some fixed point results in rectangular metric spaces." Annals of Mathematics and Physics 6, no. 2 (2023): 108–13. http://dx.doi.org/10.17352/amp.000089.

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After motivation from Geraghty-type contractions and of Farhan, et al. we define α-admissible mappings and demonstrate the fixed point theorems for the above-mentioned contractions in rectangular metric space in this study. In the end, we discuss some consequences of our results as corollaries. 2010 MSC: 47H10, 54H25.

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A.S., Saluja, and Yadav Asmita. "On Fixed Points in B-Rectangular Metric Spaces." International Journal of Mathematics and Computer Research 13, no. 05 (2025): 5187–89. https://doi.org/10.5281/zenodo.15432218.

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This paper presents fixed point results in b-rectangular metric spaces. The results obtained expand and generalize several well-established finding in the existing literature.  <strong>2020 Mathematics Subject Classification</strong>: Primary: 54H25; Secondary: 54E50, 47H10.

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