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Journal articles on the topic 'Generalized Metric Spaces'

Author: Grafiati

Published: 5 October 2024

Last updated: 31 July 2025

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1

Ur Rehman, Saif, Abeer Jaradat, Sidra Akbar, Sidra Atta, Bosko Damjanovic, and Mohammed Jaradat. "GENERALIZED UNIQUE FIXED POINT RESULTS IN GENERALIZED FUZZY METRIC SPACES." Journal of Mathematical Analysis 15, no. 6 (2024): 30–46. https://doi.org/10.54379/jma-2024-6-3.

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This paper aims to establish some basic properties and generalized unique fixed point (FP) theorems on generalized fuzzy metric spaces (GFM-spaces) by using the rectangular property of the generalized fuzzy metric without the continuity of self-mappings. In support of our results, we present nontrivial illustrative unique FP examples for single-valued contractive type mappings on complete GFM-spaces. This work can be further improved and extend for different types of single-valued mappings on GFM-spaces with supportive trivial and nontrivial illustrative examples.

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2

Kucuk, Serife, and Hafize Gumus. "GENERALIZED METRIC SPACES AND LACUNARY STATISTICAL CONVERGENCE." Journal of Mathematical Analysis 13, no. 6 (2002): 16–24. https://doi.org/10.54379/jma-2022-6-2.

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In this study, we examine lacunary statistical convergence on g−metric spaces. g−metric spaces are metric spaces that have been gener- alized by defining the distance concept between n + 1 points. In this sense, we denote the relationships between gS, gSθ , gNθ and gC1 which we have found to be related to each other.

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3

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

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4

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 (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 be

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5

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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6

Hussain, Nawab, Abdulaziz Alofi, and Osama Alhindi. "COMMON FIXED POINT RESULTS FOR GENERALIZED CONTRACTIONS IN M-METRIC SPACES." Journal of Mathematical Analysis 15, no. 6 (2024): 58–70. https://doi.org/10.54379/jma-2024-6-5.

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The concept of M-metric generalizes both partial metric and conventional metric concepts. The aim of this paper is to investigate certain fixed and common fixed point results for generalized contractive mappings in Mmetric spaces. Moreover, we demonstrate the applicability of our results by providing specific examples. Our findings extend several existing results in the literature, broadening them from conventional metric spaces to M-metric spaces.

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7

La Rosa, Vincenzo, та Pasquale Vetro. "Common fixed points for α-ψ-φ-contractions in generalized metric spaces". Nonlinear Analysis: Modelling and Control 19, № 1 (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 i

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8

Yang, Hui. "Meir–Keeler Fixed-Point Theorems in Tripled Fuzzy Metric Spaces." Mathematics 11, no. 24 (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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9

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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10

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

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11

Wongsasinchai, Paiwan, and Warut Kitcharoen. "GENERALIZED QUASI-CONTRACTION FOR DISLOCATED QUASI-METRIC SPACES." Journal of Inequalities and Special Functions 14, no. 3 (2023): 7–16. https://doi.org/10.54379/jiasf-2023-3-2.

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In this paper, T-orbitally complete dislocated quasi-metric spaces are utilized to validate fixed point results for freshly developed Geraghty quasi-contraction type mappings. The Geraghty quasi-contraction type mappings generalize Ciric’s quasi-contraction mappings and other Geraghty quasicontractive type mappings in the literature. Without establishing a continuity condition on the mapping, fixed point results are obtained, generalizing some relevant work in the literature.

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12

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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13

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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14

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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15

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 to

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16

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

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17

Kisi, Omer, Burak Cakal, and Mehmet Gurdal. "ON IDEAL CONVERGENCE OF SEQUENCES IN QUATERNION VALUED GENERALIZED METRIC SPACES." Journal of Mathematical Analysis 15, no. 5 (2024): 19–42. https://doi.org/10.54379/jma-2024-5-2.

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The primary objective of this study is to introduce the notion of ideal convergence in quaternion-valued generalized metric spaces. We define Iconvergence and I ∗-convergence in these spaces and establish their equivalence through the definition of property (AP). Furthermore, we introduce I-Cauchy and I ∗-Cauchy sequences, adapting classically theorems to suit quaternionvalued generalized metric spaces. We also present I-statistical convergence, I-lacunary statistical convergence, strong I-Ces`aro summability, strong Ilacunary summability, [V, λ](I)-summability, and I-λ-statistically convergen

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18

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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19

KAYODE, ADEWALE OLUSOLA, OLALERU JOHNSON, OLAOLUWA HALLOWED та AKEWE HUDSON. "Fixed point theorems on a γ-generalized quasi-metric spaces". Creative Mathematics and Informatics 28, № 2 (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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20

Abbas, Mujahid, Bahru Leyew та Safeer Khan. "A new Ф-generalized quasi metric space with some fixed point results and applications". Filomat 31, № 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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21

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

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22

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

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23

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

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24

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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25

Pandiselvi, R., M. Jeyaraman, and A. Ramachandran. "Compatible maps of type \(\beta\) in intuitionistic generalized fuzzy metric spaces." Open Journal of Discrete Applied Mathematics 5, no. 3 (2022): 1–12. https://doi.org/10.30538/psrp-odam2022.075.

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This paper presents several fixed point theorems for intuitionistic generalized fuzzy metric spaces with an implicit relation. Specifically, we utilize compatible maps of type \(\beta\) in intuitionistic generalized fuzzy metric spaces to derive our fixed point theorems. Our results not only extend but also generalize some fixed point theorems that were previously established in complete fuzzy metric spaces. This is achieved by introducing a novel technique, which enhances the applicability and scope of the existing fixed point theorems.

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26

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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27

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 (2013): 203–31. http://dx.doi.org/10.1007/s10474-013-0304-1.

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28

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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29

Soni, Bhawna, and Dr Abha Tenguria. "Expansion mapping in controlled metric space and extended B-metric space." International Journal of Multidisciplinary Research and Growth Evaluation 6, no. 1 (2025): 854–59. https://doi.org/10.54660/.ijmrge.2025.6.1.854-859.

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This paper delves into the intricate study of expansion mappings within the frameworks of controlled metric spaces and extended B-metric spaces. Expansion mappings, known for their crucial role in fixed-point theory and iterative processes, are examined under the lens of these generalized metric spaces to uncover their distinct properties and extended applicability. Controlled metric spaces, which incorporate a dynamic control function to modulate the distance measurements, offer a refined approach to traditional metric space concepts. This flexibility allows for a more nuanced understanding o

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30

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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31

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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32

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 (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 informa

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33

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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34

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 (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, 53

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35

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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36

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 (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 partia

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37

Latif, Abdul, Chirasak Mongkolkeha та 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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38

LU, GUANGHUI, and SHUANGPING TAO. "GENERALIZED MORREY SPACES OVER NONHOMOGENEOUS METRIC MEASURE SPACES." Journal of the Australian Mathematical Society 103, no. 2 (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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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 (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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40

Abtahi, Mortaza, Zoran Kadelburg та Stojan Radenovic. "Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces". Applied General Topology 19, № 2 (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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41

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

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42

Bansal, Dinesh Rani, and Reetu Reetu. "Common Fixed Point Theorems Involving Cubic Terms of d(x, y) in b-Metric Spaces." Indian Journal Of Science And Technology 18, no. 3 (2025): 184–92. https://doi.org/10.17485/ijst/v18i3.1590.

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Objective/Aim: To establish the existence and uniqueness of fixed points for self maps in b-metric spaces. Methods: We have used generalized 𝜑-weak contractive condition involving cubic terms of d(x, y) and weak compatibility of two maps in the setting of b-metric spaces. Findings: Some fixed point theorems for a self map and common fixed point theorems for two maps have been proved and some suitable examples are also given to justify the proven results. Novelty: In b-metric spaces, the existence of fixed points for mappings satisfying generalized 𝜑-weak contractive conditions involving cubic

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43

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 (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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44

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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45

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 (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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Chiroma, Rhoda, Mohammed Shehu Shagari, and Ezra Emmanuel Tanto. "Fixed Results on Generalized Weakly Quasi-Type Contractive Operators." Mikailalsys Journal of Mathematics and Statistics 3, no. 3 (2025): 530–47. https://doi.org/10.58578/mjms.v3i3.6046.

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This study introduces and investigates generalized weakly quasi-type contractive operators within the context of b-metric-like spaces, aiming to establish rigorous conditions for the existence and uniqueness of fixed points. While weakly contractive mappings have been widely examined in standard metric spaces, their behavior in b-metric-like spaces remains underexplored. Addressing this gap, the paper extends existing theoretical frameworks and contributes novel results relevant to this generalized setting. The proposed assertions are substantiated through non-trivial comparative examples, and

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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 (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

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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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Petrovic, Milos. "On generalized almost para-Hermitian spaces." Filomat 37, no. 25 (2023): 8719–24. http://dx.doi.org/10.2298/fil2325719p.

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Recently, a generalized almost Hermitian metric on an almost complex manifold (M, J) is determined as a generalized Riemannian metric (i.e. an arbitrary bilinear form) G which satisfies G(JX, JY) = G(X,Y), where X and Y are arbitrary vector fields on M. In the same manner we can study a generalized almost para-Hermitian metric and determine almost para-Hermitian spaces. Some properties of these spaces and special generalized almost para-Hermitian spaces including generalized para-Hermitian spaces as well as generalized nearly para-K?hler spaces are determined. Finally, a non-trivial example of

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Zhu, Chuanxi, Wenqing Xu, and Zhaoqi Wu. "Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/103764.

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We introduce the concepts of(H,ψ,Φ)-contraction and probabilistic(α,φ)-contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results.

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