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Journal articles on the topic 'Generalized Metric Spaces'

Author: Grafiati

Published: 5 October 2024

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1

BEG, ISMAT, MUJAHID ABBAS, and TALAT NAZIR. "GENERALIZED CONE METRIC SPACES." Journal of Nonlinear Sciences and Applications 03, no. 01 (February 13, 2010): 21–31. http://dx.doi.org/10.22436/jnsa.003.01.03.

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2

Ali, Basit, Hammad Ali, Talat Nazir, and Zakaria Ali. "Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces." Mathematics 11, no. 21 (October 26, 2023): 4445. http://dx.doi.org/10.3390/math11214445.

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In order to generalize classical Banach contraction principle in the setup of quasi-metric spaces, we introduce Suzuki-type contractions of quasi-metric spaces and prove some fixed point results. Further, we suggest a correction in the definition of another class of quasi-metrics known as Δ-symmetric quasi-metrics satisfying a weighted symmetry property. We discuss equivalence of various types of completeness of Δ-symmetric quasi-metric spaces. At the end, we consider the existence of fixed points of generalized Suzuki-type contractions of Δ-symmetric quasi-metric spaces. Some examples have been furnished to make sure that generalizations we obtain are the proper ones.

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3

D, Ramesh Kumar. "Generalized Rational Inequalities in Complex Valued Metric Spaces." Journal of Computational Mathematica 1, no. 2 (December 30, 2017): 121–32. http://dx.doi.org/10.26524/cm21.

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4

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 (April 10, 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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5

La Rosa, Vincenzo, and Pasquale Vetro. "Common fixed points for α-ψ-φ-contractions in generalized metric spaces." Nonlinear Analysis: Modelling and Control 19, no. 1 (January 20, 2014): 43–54. http://dx.doi.org/10.15388/na.2014.1.3.

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We establish some common fixed point theorems for mappings satisfying an α-ψ-ϕcontractive condition in generalized metric spaces. Presented theorems extend and generalize manyexisting results in the literature. Erratum to “Common fixed points for α-ψ-φ-contractions in generalized metric spaces” In Example 1 of our paper [V. La Rosa, P. Vetro, Common fixed points for α-ψ-ϕcontractions in generalized metric spaces, Nonlinear Anal. Model. Control, 19(1):43–54, 2014] a generalized metric has been assumed. Nevertheless some mistakes have appeared in the statement. The aim of this note is to correct this situation.

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6

Yang, Hui. "Meir–Keeler Fixed-Point Theorems in Tripled Fuzzy Metric Spaces." Mathematics 11, no. 24 (December 14, 2023): 4962. http://dx.doi.org/10.3390/math11244962.

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In this paper, we first propose the concept of a family of quasi-G-metric spaces corresponding to the tripled fuzzy metric spaces (or G-fuzzy metric spaces). Using their properties, we give the characterization of tripled fuzzy metrics. Second, we introduce the notion of generalized fuzzy Meir–Keeler-type contractions in G-fuzzy metric spaces. With the aid of the proposed notion, we show that every orbitally continuous generalized fuzzy Meir–Keeler-type contraction has a unique fixed point in complete G-fuzzy metric spaces. In the end, an example illustrates the validity of our results.

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7

Karapınar, Erdal. "Discussion onα-ψContractions on Generalized Metric Spaces." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/962784.

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We discuss the existence and uniqueness of fixed points ofα-ψcontractive mappings in complete generalized metric spaces, introduced by Branciari. Our results generalize and improve several results in the literature.

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8

Zhang, Wei, and Chenxi Ouyang. "GENERALIZED CONE METRIC SPACES AND ORDERED SPACES." Far East Journal of Applied Mathematics 101, no. 2 (March 15, 2019): 101–12. http://dx.doi.org/10.17654/am101020101.

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9

Brock, Paul. "Probabilistic convergence spaces and generalized metric spaces." International Journal of Mathematics and Mathematical Sciences 21, no. 3 (1998): 439–52. http://dx.doi.org/10.1155/s0161171298000611.

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The categoryPPRS(Δ), whose objects are probabilistic pretopological spaces which satisfy an axiom(Δ)and whose morphisms are continuous mappings, is introduced. Categories consisting of generalized metric spaces as objects and contraction mappings as morphisms are embedded as full subcategories ofPPRS(Δ). The embeddings yield a description of metric spces and their most natural generalizations entirely in terms of convergence criteria.

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10

Liftaj, Silvana, Eriola Sila, and Zamir Selko. "Generalized almost Contractions on Extended Quasi-Cone B-Metric Spaces." WSEAS TRANSACTIONS ON MATHEMATICS 22 (November 29, 2023): 894–903. http://dx.doi.org/10.37394/23206.2023.22.98.

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Fixed Point Theory is among the most valued research topics nowadays. Over the years, it has been developed in three directions: by generalizing the metric space, by establishing new contractive conditions, and by applying its results to various fields such as Differential Equations, Integral Equations, Economics, etc. In this paper, we define a new class of cone metric spaces called the class of extended quasi-cone b-metric spaces. Extended quasi-cone b-metric spaces generalize cone metric spaces and quasi-cone b-metric spaces. We have studied topological issues, such as the right and left topologies, right (left) Cauchy, and convergent sequences. Furthermore, there are determined generalized τ-almost contractions, which extend the almost contractions. The highlight of this study is the investigation of the existence and uniqueness of a fixed point for some types of generalized τ-almost contractions in extended quasi-cone b-metric space. We prove some corollaries and theorems for known contractions in extended quasi-cone b-metric spaces. Our results generalize some known theorems given in literature due to the new cone metric spaces and contractions. Concrete examples illustrate theoretical outcomes. In addition, we show an application of the main results to Integral Equations, which provides the applicative side of them.

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11

SARMA, I. R., J. M. RAO2, and S. S. RAO. "CONTRACTIONS OVER GENERALIZED METRIC SPACES." Journal of Nonlinear Sciences and Applications 02, no. 03 (August 15, 2009): 180–82. http://dx.doi.org/10.22436/jnsa.002.03.06.

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12

Khamsi, M. A. "Generalized metric spaces: A survey." Journal of Fixed Point Theory and Applications 17, no. 3 (May 16, 2015): 455–75. http://dx.doi.org/10.1007/s11784-015-0232-5.

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13

Beshimov, Ruzinazar, and Dilnora Safarova. "Generalized metric spaces and hyperspaces." Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences 3, no. 2 (June 15, 2020): 269–77. http://dx.doi.org/10.56017/2181-1318.1103.

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14

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 nonlinear problems related to chemical sciences. Finally, an open question is given for generalized contractile mappings in rectangular metric spaces. Conclusions: New results are given for fixed points in rectangular metric spaces with application to some problems in chemical sciences.

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15

Kikina, Luljeta, Kristaq Kikina, and Kristaq Gjino. "A New Fixed Point Theorem on Generalized Quasimetric Spaces." ISRN Mathematical Analysis 2012 (January 26, 2012): 1–9. http://dx.doi.org/10.5402/2012/457846.

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We obtain a new fixed point theorem in generalized quasimetric spaces. This result generalizes, unify, enrich, and extend some theorems of well-known authors from metric spaces to generalized quasimetric spaces.

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16

Abbas, Mujahid, Bahru Leyew, and Safeer Khan. "A new Ф-generalized quasi metric space with some fixed point results and applications." Filomat 31, no. 11 (2017): 3157–72. http://dx.doi.org/10.2298/fil1711157a.

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In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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17

Shatanawi, Wasfi, Ahmed Al-Rawashdeh, Hassen Aydi, and Hemant Kumar Nashine. "On a Fixed Point for Generalized Contractions in Generalized Metric Spaces." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/246085.

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Lakzian and Samet (2010) studied some fixed-point results in generalized metric spaces in the sense of Branciari. In this paper, we study the existence of fixed-point results of mappings satisfying generalized weak contractive conditions in the framework of a generalized metric space in sense of Branciari. Our results modify and generalize the results of Laksian and Samet, as well as, our results generalize several well-known comparable results in the literature.

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18

Korczak-Kubiak, Ewa, Anna Loranty, and Ryszard J. Pawlak. "Baire generalized topological spaces, generalized metric spaces and infinite games." Acta Mathematica Hungarica 140, no. 3 (February 9, 2013): 203–31. http://dx.doi.org/10.1007/s10474-013-0304-1.

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19

Aydi, Hassen, Sana Hadj Amor, and Erdal Karapınar. "Berinde-Type Generalized Contractions on Partial Metric Spaces." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/312479.

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We consider generalized Berinde-type contractions in the context of partial metric spaces. Such contractions are also known as generalized almost contractions in the literature. In this paper, we extend, generalize, and enrich the results in this direction. Some examples are presented to illustrate our results.

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20

Abazari, Rasoul. "Statistical convergence in g-metric spaces." Filomat 36, no. 5 (2022): 1461–68. http://dx.doi.org/10.2298/fil2205461a.

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The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.

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21

KAYODE, ADEWALE OLUSOLA, OLALERU JOHNSON, OLAOLUWA HALLOWED, and AKEWE HUDSON. "Fixed point theorems on a γ-generalized quasi-metric spaces." Creative Mathematics and Informatics 28, no. 2 (June 19, 2019): 135–42. http://dx.doi.org/10.37193/cmi.2019.02.05.

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The concept of \gamma-generalized quasi-metric spaces is newly introduced in this paper with the symmetry assumption removed. The existence of fixed points of our newly introduced (\gamma-\phi)-contraction mappings, defined on \gamma-generalized quasi-metric spaces, is proved. Our results generalize many known related results in literature.

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22

He, S. Y., L. H. Xie, and P. F. Yan. "On *-metric spaces." Filomat 36, no. 18 (2022): 6173–85. http://dx.doi.org/10.2298/fil2218173h.

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Metric spaces are generalized by many scholars. Recently, Khatami and Mirzavaziri use a mapping called t-definer to popularize the triangle inequality and give a generalization of the notion of a metric, which is called a *-metric. In this paper, we prove that every *-metric space is metrizable. Also, we study the total boundedness and completeness of *-metric spaces.

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23

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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24

Sawano, Yoshihiro, and Tetsu Shimomura. "Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces." Georgian Mathematical Journal 25, no. 2 (June 1, 2018): 303–11. http://dx.doi.org/10.1515/gmj-2018-0018.

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Abstract In this paper, we aim to deal with the boundedness and the weak-type boundedness for the generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces, as an extension of [Y. Sawano and T. Shimomura, Boundedness of the generalized fractional integral operators on generalized Morrey spaces over metric measure spaces, Z. Anal. Anwend. 36 2017, 2, 159–190], [Y. Sawano and T. Shimomura, Generalized fractional integral operators over non-doubling metric measure spaces, Integral Transforms Spec. Funct. 28 2017, 7, 534–546] and [I. Sihwaningrum, H. Gunawan and E. Nakai, Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces, Math. Nachr., to appear].

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25

LU, GUANGHUI, and SHUANGPING TAO. "GENERALIZED MORREY SPACES OVER NONHOMOGENEOUS METRIC MEASURE SPACES." Journal of the Australian Mathematical Society 103, no. 2 (October 27, 2016): 268–78. http://dx.doi.org/10.1017/s1446788716000483.

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Let $({\mathcal{X}},d,\unicode[STIX]{x1D707})$ be a nonhomogeneous metric measure space satisfying the so-called upper doubling and the geometric doubling conditions. In this paper, the authors give the natural definition of the generalized Morrey spaces on $({\mathcal{X}},d,\unicode[STIX]{x1D707})$, and then investigate some properties of the maximal operator, the fractional integral operator and its commutator, and the Marcinkiewicz integral operator.

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26

Saleem, Naeem, Iqra Habib, and Manuel De la Sen. "Some New Results on Coincidence Points for Multivalued Suzuki-Type Mappings in Fairly Complete Spaces." Computation 8, no. 1 (March 17, 2020): 17. http://dx.doi.org/10.3390/computation8010017.

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In this paper, we introduce Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. We establish some coincidence and best proximity point results in fairly complete spaces. Also, we provide coincidence and best proximity point results in partially ordered complete metric spaces for Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. Furthermore, some examples are presented in each section to elaborate and explain the usability of the obtained results. As an application, we obtain fixed-point results in metric spaces and in partially ordered metric spaces. The results obtained in this article further extend, modify and generalize the various results in the literature.

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27

Suzuki, Tomonari. "Generalized Metric Spaces Do Not Have the Compatible Topology." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/458098.

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We study generalized metric spaces, which were introduced by Branciari (2000). In particular, generalized metric spaces do not necessarily have the compatible topology. Also we prove a generalization of the Banach contraction principle in complete generalized metric spaces.

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28

FILIP, ALEXANDRU-DARIUS. "Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory." Carpathian Journal of Mathematics 37, no. 2 (June 9, 2021): 345–54. http://dx.doi.org/10.37193/cjm.2021.02.19.

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In this paper we discuss similar problems posed by I. A. Rus in Fixed point theory in partial metric spaces (Analele Univ. de Vest Timişoara, Mat.-Inform., 46 (2008), 149–160) and in Kasahara spaces (Sci. Math. Jpn., 72 (2010), No. 1, 101–110). We start our considerations with an overview of generalized metric spaces with \mathbb{R}_+-valued distance and of generalized contractions on such spaces. After that we give some examples of conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory. Some possible applications to theoretical informatics are also considered.

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29

Li, Cece, and Dong Zhang. "On generalized metric spaces and generalized convex contractions." Fixed Point Theory 19, no. 2 (June 1, 2018): 643–58. http://dx.doi.org/10.24193/fpt-ro.2018.2.51.

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30

Latif, Abdul, Chirasak Mongkolkeha, and Wutiphol Sintunavarat. "Fixed Point Theorems for Generalizedα-β-Weakly Contraction Mappings in Metric Spaces and Applications." Scientific World Journal 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/784207.

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We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalizedα-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.

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31

Abtahi, Mortaza, Zoran Kadelburg, and Stojan Radenovic. "Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces." Applied General Topology 19, no. 2 (October 4, 2018): 189. http://dx.doi.org/10.4995/agt.2018.7409.

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<p>New fixed point and coupled fixed point theorems in partially ordered ν-generalized metric spaces are presented. Since the product of two ν-generalized metric spaces is not in general a ν-generalized metric space, a different approach is needed than in the case of standard metric spaces.</p>

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32

Suzuki, Tomonari. "Completeness of 3-generalized metric spaces." Filomat 30, no. 13 (2016): 3575–85. http://dx.doi.org/10.2298/fil1613575s.

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33

Ugwunnadi, Godwin C., Chinedu Izuchukwu, and Oluwatosin T. Mewomo. "Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space." Journal of Applied Analysis 26, no. 2 (December 1, 2020): 221–29. http://dx.doi.org/10.1515/jaa-2020-2017.

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AbstractIn this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

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34

Nicolae, Adriana, Donal O'Regan, and Adrian Petruşel. "Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph." gmj 18, no. 2 (May 2, 2011): 307–27. http://dx.doi.org/10.1515/gmj.2011.0019.

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Abstract The purpose of this paper is to present some fixed point results for self-generalized (singlevalued and multivalued) contractions in ordered metric spaces and in metric spaces endowed with a graph. Our theorems generalize and extend some recent results in the literature.

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35

Ahmed, M. A., A. Kamal, and Asmaa M. Abd-Ela. "Convergence theorems in new generalized type of metric spaces and their applications ∗." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 42, no. 2 (December 25, 2023): 180–85. http://dx.doi.org/10.48165/bpas.2023.42e.2.6.

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In the present paper we introduce a new generalized type of metric spaces called the right quasi-metric spaces. We state and prove convergence theorems to a fixed point for any map in these spaces. Finally, we give applications of our results. These results generalize the corresponding results in M. A. Ahmed and F. M. Zeyada (On con vergence of a sequence in complete metric spaces and its applications to some iterates of quasi-nonexpansive mappings, J. Math. Anal. Appl., 274(1), 458–465, 2002).

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36

Mizokami, Takemi, and Fumio Suwada. "On resolutions of generalized metric spaces." Topology and its Applications 146-147 (January 2005): 539–45. http://dx.doi.org/10.1016/j.topol.2003.10.009.

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37

Liu, Chuan, and Shou Lin. "Generalized metric spaces with algebraic structures." Topology and its Applications 157, no. 12 (August 2010): 1966–74. http://dx.doi.org/10.1016/j.topol.2010.04.010.

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38

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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39

Antoniuk, Sylwia, and Paweł Waszkiewicz. "A duality of generalized metric spaces." Topology and its Applications 158, no. 17 (November 2011): 2371–81. http://dx.doi.org/10.1016/j.topol.2011.04.013.

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40

Kumari, P. Sumati, I. Ramabhadra Sarma, and J. Madhusudana Rao. "Convergence axioms on generalized metric spaces." Afrika Matematika 28, no. 1-2 (April 20, 2016): 35–43. http://dx.doi.org/10.1007/s13370-016-0425-0.

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41

Good, Chris, and Sergio Macías. "Symmetric products of generalized metric spaces." Topology and its Applications 206 (June 2016): 93–114. http://dx.doi.org/10.1016/j.topol.2016.03.019.

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42

Mohamad, Abdul Adheem, and Tsukasa Yashiro. "TOPOLOGICAL STUDY OF GENERALIZED METRIC SPACES." JP Journal of Geometry and Topology 22, no. 2 (May 30, 2019): 165–88. http://dx.doi.org/10.17654/gt022020165.

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43

Farhat, Yasser, Amel Souhail, Vadakasi Vigneswaran, and Muthumari Krishnan. "Special Sequences on Generalized Metric Spaces." European Journal of Pure and Applied Mathematics 15, no. 4 (October 31, 2022): 1869–86. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4592.

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In this article, in a generalized metric space, we will focus on new types of sequences. We introduce three new kinds of Cauchy sequences and study their significance in generalized metric spaces. Also, we give several interesting properties of these sequences.

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44

Kabil, Mustapha, Maurice Pouzet, and Ivo G. Rosenberg. "Free monoids and generalized metric spaces." European Journal of Combinatorics 80 (August 2019): 339–60. http://dx.doi.org/10.1016/j.ejc.2018.02.008.

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45

Conant, Gabriel. "Distance structures for generalized metric spaces." Annals of Pure and Applied Logic 168, no. 3 (March 2017): 622–50. http://dx.doi.org/10.1016/j.apal.2016.10.002.

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46

Arutyunov, A. V., and S. E. Zhukovskiy. "Coincidence Points in Generalized Metric Spaces." Set-Valued and Variational Analysis 23, no. 2 (December 14, 2014): 355–73. http://dx.doi.org/10.1007/s11228-014-0312-5.

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47

Mizokami, Takemi. "On hyperspaces of generalized metric spaces." Topology and its Applications 76, no. 2 (April 1997): 169–73. http://dx.doi.org/10.1016/s0166-8641(96)00112-5.

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48

Abbas, Mujahid, Basit Ali, and Salvador Romaguera. "Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/391952.

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Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalizedF-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature.

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49

Khan, Asad Ullah, Maria Samreen, Aftab Hussain, and Hamed Al Sulami. "Best Proximity Point Results for Multi-Valued Mappings in Generalized Metric Structure." Symmetry 16, no. 4 (April 21, 2024): 502. http://dx.doi.org/10.3390/sym16040502.

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In this paper, we introduce the novel concept of generalized distance denoted as Jθ and call it an extended b-generalized pseudo-distance. With the help of this generalized distance, we define a generalized point to set distance Jθ(u,H★), a generalized Hausdorff type distance and a PJθ-property of a pair (H★,K★) of nonempty subsets of extended b-metric space (U★,ρθ). Additionally, we establish several best proximity point theorems for multi-valued contraction mappings of Nadler type defined on b-metric spaces and extended b-metric spaces. Our findings generalize numerous existing results found in the literature. To substantiate the introduced notion and validate our main results, we provide some concrete examples.

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50

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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Abstract:

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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