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Journal articles on the topic 'Rectangular metric space'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

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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2

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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3

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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4

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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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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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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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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8

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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9

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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10

Noor Riyadh Adeeb. "Partial b-Rectangular Metric Space with Some Results." Tikrit Journal of Pure Science 27, no. 2 (2022): 91–95. http://dx.doi.org/10.25130/tjps.v27i2.73.

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A new generalization of metric space called partial b-rectangular metric space is introduced. Also, the relation between this generalization and the other generalizations for example a b-rectangular metric space is given. Moreover, we have proved Banach theorem and Kannan theorem of fixed Point in partial b-rectangular metric space. Furthermore, some definitions and results dealing with partial b-rectangular metric space are discussed

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11

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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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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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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14

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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15

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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Ishtiaq, Umar, Naeem Saleem, Muhammad Farhan, Maggie Aphne, and Mohammad Showkat Rahim Chowdhury. "Fixed Point Theorems in Controlled Rectangular Modular Metric Spaceswith Solution of Fractional Differential Equations." European Journal of Pure and Applied Mathematics 18, no. 1 (2025): 5794. https://doi.org/10.29020/nybg.ejpam.v18i1.5794.

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In this paper, we establish the notion of controlled rectangular modular metric space as a generalization of modular $b-$metric space and rectangular $b-$metric space. We used contraction mappings to find the existence and uniqueness of a fixed point in the framework of controlled rectangular modular metric space. We give several non-trivial examples and show the validity of contraction mappings via graphs. At the end, we utilize our main result to solve a non-linear fractional differential equation.

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17

Thangaraj, Beaula #. "Some Common Fixed Point Results in 2-Fuzzy 2-Rectangular Metric Spaces." Mathematical statistics and engineering applications 71, no. 4 (2022): 932–40. https://doi.org/10.5281/zenodo.7505253.

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The concept of fuzzy set was introduced by L.A.Zadeh(1965) [10] in his seminal paper. Shen et al.(2012)[8] introduced the notion of control function of fuzzy metric spaces. Nagoor Gani and Mohamed Althaf (2018)[5] established some results on fixed point theorem by using control function. Bose and Sahani (1987)[1] have studied the fixed point theorem for fuzzy mapping coincidence points. Fang (1992) [2] developed fixed point theorems for different types of mapping. Soni (2018)[7] came with a new class of implict function to prove the concept of fixed point theorems in fuzzy metric space and its

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18

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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19

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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20

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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21

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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22

George, R., S. Radenović, K. P. Reshma, and S. Shukla. "Rectangular b-metric space and contraction principles." Journal of Nonlinear Sciences and Applications 08, no. 06 (2015): 1005–13. http://dx.doi.org/10.22436/jnsa.008.06.11.

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23

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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24

Asim, Mohammad, and Rachna Rathee. "FIXED POINT RESULTS IN ORDERED EXTENDED RECTANGULAR b- METRIC SPACE WITH GERAGHTY-WEAK CONTRACTION." jnanabha 53, no. 02 (2023): 95–105. http://dx.doi.org/10.58250/jnanabha.2023.53212.

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In this paper, we prove some ordered-theoretic fixed point results for a Geraghty-weak contraction on an ordered extended rectangular b􀀀metric spaces. Our results generalize several core results of the existing literature especially involving Geraghty-weak contractions and the results proved in extended rectangular b-metric space. Some examples are also furnished to exhibits the utility of our main results.

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25

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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26

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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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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MAYBANK, STEPHEN J. "THE FISHER–RAO METRIC FOR LINES IN A CONVEX IMAGE." International Journal of Pattern Recognition and Artificial Intelligence 21, no. 06 (2007): 977–94. http://dx.doi.org/10.1142/s021800140700582x.

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The Fisher–Rao metric on the parameter space for the set of lines in a two-dimensional convex image is approximated under the assumption that the errors in the measurements are small. The volume of the parameter space under the approximating metric is proportional to the area of the image under the Euclidean metric. In the case of a rectangular image, expressions for the approximating metric are obtained and an algorithm is given for sampling the parameter space. The sample points are used in an algorithm for detecting lines in a rectangular image. Experimental results are reported. In the cas

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Patil, Jayshree, Basel Hardan, Ahmed A. Hamoud, Amol Bachhav, Homan Emadifar, and Hatira Günerhan. "Generalization Contractive Mappings on Rectangular b -Metric Space." Advances in Mathematical Physics 2022 (May 14, 2022): 1–10. http://dx.doi.org/10.1155/2022/7291001.

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In this paper, we introduce new coincidence fixed point theorems for generalized ϕ , ψ -contractive mappings fulfilling kind of an admissibility provision in a Hausdorff b -rectangular metric space with the support of C-functions. We applied our results to establish the existence of a solution for some integralitions. Finally, an example is presented to clarify our theorem.

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Bhutia, Jigmi Dorjee, and Kalishankar Tiwary. "Common Fixed Point on Cone Rectangular Metric Space." International Journal of Mathematics Trends and Technology 56, no. 5 (2018): 335–43. http://dx.doi.org/10.14445/22315373/ijmtt-v56p545.

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Oztunc, Simge, Ali Mutlu, and Sedat Aslan. "Some Kannan type fixed point results in rectangular soft metric space and an application of fixed point for thermal science problem." Thermal Science 23, Suppl. 1 (2019): 215–25. http://dx.doi.org/10.2298/tsci181102035o.

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The intention of current study to survey Kannan type mappings for rectangular soft metric space. Some Kannan type results are obtained by using rectangular soft metric and an application for thermal science problem is presented.

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Singh, P., and V. Singh. "FIXED POINT THEOREMS IN A WEIGHTED RECTANGULAR b-METRIC SPACE." Advances in Mathematics: Scientific Journal 10, no. 4 (2021): 2157–65. http://dx.doi.org/10.37418/amsj.10.4.30.

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In this paper, we provide a generalization of a rectangular b-metric space by relaxing the rectangular inequality to include unequal weights. We provide examples and restrictions for the Lipschitz constant enabling convergence of some sequences in the proof of some fixed point theorems.

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Mani, Gunaseelan, Rajagopalan Ramaswamy, Arul Joseph Gnanaprakasam, Ola A. Ashour Abdelnaby, Slobodan Radojevic, and Stojan Radenović. "Solution of Integral Equation with Neutrosophic Rectangular Triple Controlled Metric Spaces." Symmetry 14, no. 10 (2022): 2074. http://dx.doi.org/10.3390/sym14102074.

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In this paper, we introduce the notion of neutrosophic rectangular triple-controlled metric space, relaxing the symmetry requirement of neutrosophic metric spaces, by replacing triangular inequalities with rectangular inequalities, and prove fixed point theorems. We have derived several interesting results for contraction mappings supplemented with non-trivial examples. The derived results have been applied to prove the existence of a unique analytical solution as well as a closed form of the unique solution to the integral equation.

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Secelean, Nicolae Adrian, Dariusz Wardowski та Mi Zhou. "The Sehgal’s Fixed Point Result in the Framework of ρ-Space". Mathematics 10, № 3 (2022): 459. http://dx.doi.org/10.3390/math10030459.

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In this paper, we prove a fixed point theorem of Sehgal type (see Sehgal, V.M., Proc Amer Math Soc 23: 631–634, 1969) in a more general setting of ρ-space (see Secelean, N.A. and Wardowski, D., Results Math, 72: 919–935, 2017). In this way, we can find, as particular cases, some results of Sehgal type in metric, b-metric and rectangular b-metric spaces.

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Hammad, Hasanen A., Hassen Aydi, and Yaé Ulrich Gaba. "Exciting Fixed Point Results on a Novel Space with Supportive Applications." Journal of Function Spaces 2021 (January 27, 2021): 1–12. http://dx.doi.org/10.1155/2021/6613774.

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The goal of this paper is to present a new space, a complex valued controlled rectangular b -metric space (for short, υ ℂ -metric space). Some examples and topological properties of υ ℂ -metric spaces are given. Also, some related common fixed point results are discussed. Our results generalize a lot of works in this direction. Moreover, we apply the theoretical results to find a unique solution of a complex valued Atangana-Baleanu fractional integral operator and a system of complex linear equations. Finally, a numerical example to find the current that passes through the RLC circuit is illus

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Mitrović, Zoran D. "On an open problem in rectangular b-metric space." Journal of Analysis 25, no. 1 (2017): 135–37. http://dx.doi.org/10.1007/s41478-017-0036-7.

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Reddy, Pagidi Mallikarjun. "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. http://dx.doi.org/10.17485/ijst/v16i32.1303.

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Baradol, Pravin, Jelena Vujaković, Dhananjay Gopal, and Stojan Radenović. "On Some New Results in Graphical Rectangular b-Metric Spaces." Mathematics 8, no. 4 (2020): 488. http://dx.doi.org/10.3390/math8040488.

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In this paper, we provide an approach to establish the Banach contraction principle ( for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019).

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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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Souayah, Nizar, and Mehdi Mrad. "Some Fixed Point Results on Rectangular Metric-Like Spaces Endowed with a Graph." Symmetry 11, no. 1 (2018): 18. http://dx.doi.org/10.3390/sym11010018.

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The objective of this paper is to establish the existence and uniqueness of fixed points on rectangular metric-like spaces endowed with a graph. We introduce the notion of some generalized G-contractions principle. The usefulness of the considered metric space in real work is highlighted. The obtained results generalize some notes in the literature. Some examples are presented to support the main results.

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Kari, Abdelkarim, Mohamed Rossafi, El Miloudi Marhrani та Mohamed Aamri. "New Fixed Point Theorems for θ ‐ ϕ -Contraction on Rectangular b -Metric Spaces". Abstract and Applied Analysis 2020 (16 жовтня 2020): 1–12. http://dx.doi.org/10.1155/2020/8833214.

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The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions. In this paper, inspired by the concept of θ ‐ ϕ -contraction in metric spaces, introduced by Zheng et al., we present the notion of θ ‐ ϕ -contraction in b -rectangular metric spaces and study the existence and uniqueness of a fixed point for the mappings in this space. Our results improve many existing results.

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Asim, Mohammad, Samad Mujahid, and Izhar Uddin. "Meir-Keeler Contraction In Rectangular M−Metric Space." Topological Algebra and its Applications 9, no. 1 (2021): 96–104. http://dx.doi.org/10.1515/taa-2021-0106.

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Abstract In this paper, we prove some fixed point theorems for a Meir-Keeler type Contraction in rectangular M−metric space. Thus, our results extend and improve very recent results in fixed point theory.

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Patil, Jayshree, Basel Hardan, Ahmed A. Hamoud, Amol Bachhav, Homan Emadifar, and Hatira Günerhan. "Corrigendum to “Generalization Contractive Mappings on Rectangular b-Metric Space”." Advances in Mathematical Physics 2022 (October 14, 2022): 1. http://dx.doi.org/10.1155/2022/9761017.

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44

Mani, Gunaseelan, Arul Joseph Gnanaprakasam, Vidhya Varadharajan, and Fahd Jarad. "Solving an integral equation vian orthogonal neutrosophic rectangular metric space." AIMS Mathematics 8, no. 2 (2023): 3791–825. http://dx.doi.org/10.3934/math.2023189.

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<abstract><p>In this paper, we introduce the notion of an orthogonal neutrosophic rectangular metric space and prove fixed point theorems. We extend some of the well-known results in the literature. As applications of the main results, we apply our main results to show the existence of a unique solution.</p></abstract>

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45

Kuz’mich, V. I., L. V. Kuzmich, A. G. Savchenko, and K. V. Valko. "Analytical and geometric interpretation of the flat arrangement of points by means of metric geometry in the study of metric spaces." Journal of Physics: Conference Series 2871, no. 1 (2024): 012006. http://dx.doi.org/10.1088/1742-6596/2871/1/012006.

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Abstract When studying metric spaces, students of higher education often have difficulties with understanding the basic concepts and properties of these spaces. This, to a large extent, is a consequence of the significant level of formalization of such concepts on the one hand, and the preservation of the corresponding formulations and names familiar to students from a school mathematics course. To overcome these difficulties, it is advisable to use methods of geometric interpretation and visualization of these properties. At the same time, it is appropriate to use elements of metric geometry.

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JLELI, MOHAMED, and BESSEM SAMET. "THE KANNANS FIXED POINT THEOREM IN A CONE RECTANGULAR METRIC SPACE." Journal of Nonlinear Sciences and Applications 02, no. 03 (2009): 161–67. http://dx.doi.org/10.22436/jnsa.002.03.03.

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47

Rana, K., and A. Kumar Garg. "KANNAN-TYPE FIXED POINT RESULTS IN EXTENDED RECTANGULAR B-METRIC SPACE." Advances in Mathematics: Scientific Journal 9, no. 8 (2020): 5491–99. http://dx.doi.org/10.37418/amsj.9.8.19.

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48

Boito, Paola, and Jean-Pierre Dedieu. "The Condition Metric in the Space of Rectangular Full Rank Matrices." SIAM Journal on Matrix Analysis and Applications 31, no. 5 (2010): 2580–602. http://dx.doi.org/10.1137/08073874x.

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Horvat-Marc, Andrei, Mariana Cufoian, Adriana Mitre, and Ioana Taşcu. "Fixed Point Theorems in Rectangular b-Metric Space Endowed with a Partial Order." Axioms 12, no. 11 (2023): 1050. http://dx.doi.org/10.3390/axioms12111050.

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The purpose of this paper is to present some fixed-point results for self-generalized contractions in ordered rectangular b-metric spaces. We also provide some examples that illustrate the non-triviality and richness of this area of research.

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50

Nazam, Muhammad, Anam Arif, Hasan Mahmood, and Sang Og Kim. "Fixed Point Problems in Cone Rectangular Metric Spaces with Applications." Journal of Function Spaces 2020 (September 10, 2020): 1–10. http://dx.doi.org/10.1155/2020/8021234.

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In this paper, we introduce an ordered implicit relation and investigate some new fixed point theorems in a cone rectangular metric space subject to this relation. Some examples are presented as illustrations. We obtain a homotopy result as an application. Our results generalize and extend several fixed point results in literature.

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