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Journal articles on the topic 'Analysis on metric spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 March 2023

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1

Beg, Ismat. "Ordered Convex Metric Spaces." Journal of Function Spaces 2021 (October 25, 2021): 1–4. http://dx.doi.org/10.1155/2021/7552451.

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The aim of this article is to introduce a new notion of ordered convex metric spaces and study some basic properties of these spaces. Several characterizations of these spaces are proven that allow making geometric interpretations of the new concepts.

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2

Lu, Yufeng, Dachun Yang, and Wen Yuan. "Morrey-Sobolev Spaces on Metric Measure Spaces." Potential Analysis 41, no. 1 (September 11, 2013): 215–43. http://dx.doi.org/10.1007/s11118-013-9370-9.

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3

Bonk, Mario, Luca Capogna, Piotr Hajlasz, Nageswari Shanmugalingam, and Jeremy T. Tyson. "Analysis in Metric Spaces." Notices of the American Mathematical Society 67, no. 02 (February 1, 2020): 1. http://dx.doi.org/10.1090/noti2030.

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4

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 probability distribution of triangular inequalities in metric space axioms. Nontrivial examples, some fixed point results, and an application to the integral equation are imparted in this manuscript.

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5

EASWARAMOORTHY, D., and R. UTHAYAKUMAR. "ANALYSIS ON FRACTALS IN FUZZY METRIC SPACES." Fractals 19, no. 03 (September 2011): 379–86. http://dx.doi.org/10.1142/s0218348x11005543.

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In this paper, we investigate the fractals generated by the iterated function system of fuzzy contractions in the fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard fuzzy metric spaces by using the fuzzy Banach contraction theorem. In addition to that, we discuss some results on fuzzy fractals such as Collage Theorem and Falling Leaves Theorem in the standard fuzzy metric spaces with respect to the standard Hausdorff fuzzy metrics.

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6

Naimpally, S. A., Z. Piotrowski, and E. J. Wingler. "Plasticity in metric spaces." Journal of Mathematical Analysis and Applications 313, no. 1 (January 2006): 38–48. http://dx.doi.org/10.1016/j.jmaa.2005.04.070.

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7

Hussain, Aftab, Umar Ishtiaq, Khalil Ahmed, and Hamed Al-Sulami. "On Pentagonal Controlled Fuzzy Metric Spaces with an Application to Dynamic Market Equilibrium." Journal of Function Spaces 2022 (January 11, 2022): 1–8. http://dx.doi.org/10.1155/2022/5301293.

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In this manuscript, we coined pentagonal controlled fuzzy metric spaces and fuzzy controlled hexagonal metric space as generalizations of fuzzy triple controlled metric spaces and fuzzy extended hexagonal b-metric spaces. We use a control function in fuzzy controlled hexagonal metric space and introduce five noncomparable control functions in pentagonal controlled fuzzy metric spaces. In the scenario of pentagonal controlled fuzzy metric spaces, we prove the Banach fixed point theorem, which generalizes the Banach fixed point theorem for the aforementioned spaces. An example is offered to support our main point. We also presented an application to dynamic market equilibrium.

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8

Yonghui, Cao, and Zhou Jiang. "Morrey Spaces for Nonhomogeneous Metric Measure Spaces." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/196459.

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The authors give a definition of Morrey spaces for nonhomogeneous metric measure spaces and investigate the boundedness of some classical operators including maximal operator, fractional integral operator, and Marcinkiewicz integral operators.

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9

Puvar, Sejal V., and R. G. Vyas. "´CIRI´C-TYPE RESULTS IN QUASI-METRIC SPACES AND 𝐺-METRIC SPACES USING SIMULATION FUNCTION." Issues of Analysis 29, no. 2 (June 2022): 72–90. http://dx.doi.org/10.15393/j3.art.2022.11230.

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10

Li, Shu-Fang, Fei He, and Shu-Min Lu. "Kaleva-Seikkala’s Type Fuzzy b -Metric Spaces and Several Contraction Mappings." Journal of Function Spaces 2022 (July 23, 2022): 1–13. http://dx.doi.org/10.1155/2022/2714912.

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In this paper, we introduce the concept of Kaleva-Seikkala’s type fuzzy b -metric spaces as a generalization of the notion of b -metric spaces and fuzzy metric spaces. In such spaces, we establish Banach type, Reich type, and Chatterjea type fixed-point theorems, which improve the relevant results in fuzzy metric spaces. Two technical lemmas are employed to ensure that a Picard sequence is a Cauchy sequence. Finally, various applications are given to testify the fact that our main theorems extend the cases of b -metric spaces.

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11

Grafakos, Loukas, Liguang Liu, Diego Maldonado, and Dachun Yang. "Multilinear analysis on metric spaces." Dissertationes Mathematicae 497 (2014): 1–121. http://dx.doi.org/10.4064/dm497-0-1.

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12

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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13

Gol'dshtein, Vladimir, and Marc Troyanov. "Capacities in metric spaces." Integral Equations and Operator Theory 44, no. 2 (June 2002): 212–42. http://dx.doi.org/10.1007/bf01217533.

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14

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

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

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15

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

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

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16

George, Reny, Ivan D. Aranđelović, Vesna Mišić, and Zoran D. Mitrović. "Some Fixed Points Results in b -Metric and Quasi b -Metric Spaces." Journal of Function Spaces 2022 (January 22, 2022): 1–6. http://dx.doi.org/10.1155/2022/1803348.

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We present a fixed point result in quasi b -metric spaces. Our result generalizes recent fixed point results obtained by Aleksić et al., Dung and Hang, Jovanović et al., Sarwar, and Rahman and classical results obtained by Hardy, Rogers, and Ćirić. Also, we obtain a common fixed point result in b -metric spaces. As a special case, we get a result of Ćirić and Wong.

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17

Ren, Jiagang, and Xicheng Zhang. "Topologies on homeomorphism spaces of certain metric spaces." Journal of Mathematical Analysis and Applications 318, no. 1 (June 2006): 32–36. http://dx.doi.org/10.1016/j.jmaa.2005.05.019.

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18

Mora, G., and D. A. Redtwitz. "Densifiable metric spaces." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 105, no. 1 (February 1, 2011): 71–83. http://dx.doi.org/10.1007/s13398-011-0005-y.

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19

Javed, Khalil, Fahim Uddin, Hassen Aydi, Muhammad Arshad, Umar Ishtiaq, and Habes Alsamir. "On Fuzzy b-Metric-Like Spaces." Journal of Function Spaces 2021 (March 13, 2021): 1–9. http://dx.doi.org/10.1155/2021/6615976.

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The aim of this manuscript is to introduce the concept of fuzzy b-metric-like spaces and discuss some related fixed point results. Some examples are imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the obtained results, an application is provided to solve a first kind of Fredholm type integral equations.

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20

Han, Bang-Xian. "Conformal Transformation on Metric Measure Spaces." Potential Analysis 51, no. 1 (May 16, 2018): 127–46. http://dx.doi.org/10.1007/s11118-018-9705-7.

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21

Hebisch, W., and B. Zegarliński. "Coercive inequalities on metric measure spaces." Journal of Functional Analysis 258, no. 3 (February 2010): 814–51. http://dx.doi.org/10.1016/j.jfa.2009.05.016.

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22

Li, Hanfeng. "Metric aspects of noncommutative homogeneous spaces." Journal of Functional Analysis 257, no. 7 (October 2009): 2325–50. http://dx.doi.org/10.1016/j.jfa.2009.05.021.

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23

Amini, A., M. Fakhar, and J. Zafarani. "KKM mappings in metric spaces." Nonlinear Analysis: Theory, Methods & Applications 60, no. 6 (March 2005): 1045–52. http://dx.doi.org/10.1016/j.na.2004.10.003.

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24

Björn, Anders, Jana Björn, Tero Mäkäläinen, and Mikko Parviainen. "Nonlinear balayage on metric spaces." Nonlinear Analysis: Theory, Methods & Applications 71, no. 5-6 (September 2009): 2153–71. http://dx.doi.org/10.1016/j.na.2009.01.051.

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25

Aubin, Jean-Pierre. "Mutational equations in metric spaces." Set-Valued Analysis 1, no. 1 (1993): 3–46. http://dx.doi.org/10.1007/bf01039289.

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26

Indumathi, V. "Metric Projections and Polyhedral Spaces." Set-Valued Analysis 15, no. 3 (November 25, 2006): 239–50. http://dx.doi.org/10.1007/s11228-006-0036-2.

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27

Okon, T. "Choquet Theory in Metric Spaces." Zeitschrift für Analysis und ihre Anwendungen 19, no. 2 (2000): 303–14. http://dx.doi.org/10.4171/zaa/952.

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28

Calcaterra, Craig, and David Bleecker. "Generating Flows on Metric Spaces." Journal of Mathematical Analysis and Applications 248, no. 2 (August 2000): 645–77. http://dx.doi.org/10.1006/jmaa.2000.6948.

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29

Maciejewski, Mateusz. "Inward contractions on metric spaces." Journal of Mathematical Analysis and Applications 330, no. 2 (June 2007): 1207–19. http://dx.doi.org/10.1016/j.jmaa.2006.08.025.

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30

Jost, J�rgen. "Equilibrium maps between metric spaces." Calculus of Variations and Partial Differential Equations 2, no. 2 (May 1994): 173–204. http://dx.doi.org/10.1007/bf01191341.

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31

Ismagilov, R. S. "Minimal widths of metric spaces." Functional Analysis and Its Applications 33, no. 4 (October 1999): 270–79. http://dx.doi.org/10.1007/bf02467110.

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32

Pant, Rajendra, Rahul Shukla, H. K. Nashine, and R. Panicker. "Some New Fixed Point Theorems in Partial Metric Spaces with Applications." Journal of Function Spaces 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/1072750.

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Recently, a number of fixed point theorems for contraction type mappings in partial metric spaces have been obtained by various authors. Most of these theorems can be obtained from the corresponding results in metric spaces. The purpose of this paper is to present certain fixed point results for single and multivalued mappings in partial metric spaces which cannot be obtained from the corresponding results in metric spaces. Besides discussing some useful examples, an application to Volterra type system of integral equations is also discussed.

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33

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

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

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34

VEOMETT, E., and K. WILDRICK. "SPACES OF SMALL METRIC COTYPE." Journal of Topology and Analysis 02, no. 04 (December 2010): 581–97. http://dx.doi.org/10.1142/s1793525310000422.

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Mendel and Naor's definition of metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz is equivalent to an ultrametric space having infimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov–Hausdorff limits, and use these facts to establish a partial converse of the main result.

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35

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

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

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36

Aydi, Hassen, and Bessem Samet. "On Some Metric Inequalities and Applications." Journal of Function Spaces 2020 (October 5, 2020): 1–6. http://dx.doi.org/10.1155/2020/3842879.

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We derive a new inequality in metric spaces and provide its geometric interpretation. Some applications of our result are given, including metric inequalities in Lebesgue spaces, matrices inequalities, multiplicative metric inequalities, and partial metric inequalities. Our main result is a generalization of that obtained by Dragomir and Gosa.

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37

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

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

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38

Zidan, A. M. "S ∗ p ‐ b -Partial Metric Spaces with some Results in Common Fixed Point Theorems." Journal of Function Spaces 2021 (May 15, 2021): 1–9. http://dx.doi.org/10.1155/2021/5586936.

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In this paper, we introduce the notion of S ∗ P ‐ b -partial metric spaces which is a generalization each of S ‐ b -metric spaces and partial-metric space. Also, we study and prove some topological properties, to know the convergence of the sequences and Cauchy sequence. Finally, we study a new common fixed point theorem in these spaces.

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39

Agarwal, Ravi P., Hamed H. Alsulami, Erdal Karapınar, and Farshid Khojasteh. "Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/171624.

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Very recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces.

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40

Garai, Hiranmoy, Lakshmi Kanta Dey, Pratikshan Mondal, and Stojan Radenović. "Some remarks on bv(s)-metric spaces and fixed point results with an application." Nonlinear Analysis: Modelling and Control 25, no. 6 (November 1, 2020): 1015–34. http://dx.doi.org/10.15388/namc.2020.25.20559.

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We compare the newly defined bv(s)-metric spaces with several other abstract spaces like metric spaces, b-metric spaces and show that some well-known results, which hold in the latter class of spaces, may not hold in bv(s)-metric spaces. Besides, we introduce the notions of sequential compactness and bounded compactness in the framework of bv(s)-metric spaces. Using these notions, we prove some fixed point results involving Nemytzki–Edelstein type mappings in this setting, from which several comparable fixed point results can be deduced. In addition to these, we find some existence and uniqueness criteria for the solution to a certain type of mixed Fredholm–Volterra integral equations.

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41

Shobkolaei, Nabiollah, Shaban Sedghi, Jamal Rezaei Roshan, and Nawab Hussain. "Suzuki-Type Fixed Point Results in Metric-Like Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/143686.

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We demonstrate a fundamental lemma for the convergence of sequences in metric-like spaces, and by using it we prove some Suzuki-type fixed point results in the setup of metric-like spaces. As an immediate consequence of our results we obtain certain recent results in partial metric spaces as corollaries. Finally, three examples are presented to verify the effectiveness and applicability of our main results.

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42

Ali, Muhammad Usman, Yajing Guo, Fahim Uddin, Hassen Aydi, Khalil Javed, and Zhenhua Ma. "On R -Partial b -Metric Spaces and Related Fixed Point Results with Applications." Journal of Function Spaces 2020 (December 1, 2020): 1–8. http://dx.doi.org/10.1155/2020/6671828.

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In this paper, we introduce the notion of R -partial b -metric spaces and prove some related fixed point results in the context of this notion. We also discuss an example to validate our result. Finally, as applications, we evince the importance of our work by discussing some fixed point results on graphical-partial b -metric spaces and on partially-ordered-partial b -metric spaces.

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43

Ranjbar-Motlagh, Alireza. "Besov type function spaces defined on metric-measure spaces." Journal of Mathematical Analysis and Applications 505, no. 2 (January 2022): 125508. http://dx.doi.org/10.1016/j.jmaa.2021.125508.

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44

Aïssaoui, Noureddine. "Another extension of Orlicz-Sobolev spaces to metric spaces." Abstract and Applied Analysis 2004, no. 1 (2004): 1–26. http://dx.doi.org/10.1155/s1085337504309012.

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We propose another extension of Orlicz-Sobolev spaces to metric spaces based on the concepts of theΦ-modulus andΦ-capacity. The resulting spaceNΦ1is a Banach space. The relationship betweenNΦ1andMΦ1(the first extension defined in Aïssaoui (2002)) is studied. We also explore and compare different definitions of capacities and give a criterion under whichNΦ1is strictly smaller than the Orlicz spaceLΦ.

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45

Avilés, Antonio, and Gonzalo Martínez-Cervantes. "Complete metric spaces with property (Z) are length spaces." Journal of Mathematical Analysis and Applications 473, no. 1 (May 2019): 334–44. http://dx.doi.org/10.1016/j.jmaa.2018.12.051.

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46

Tamássy, Lajos. "Relation between metric spaces and Finsler spaces." Differential Geometry and its Applications 26, no. 5 (October 2008): 483–94. http://dx.doi.org/10.1016/j.difgeo.2008.04.007.

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47

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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48

Gamboa, Fabrice, Thierry Klein, Agnès Lagnoux, and Leonardo Moreno. "Sensitivity analysis in general metric spaces." Reliability Engineering & System Safety 212 (August 2021): 107611. http://dx.doi.org/10.1016/j.ress.2021.107611.

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49

Käenmäki, Antti, Tapio Rajala, and Ville Suomala. "Local multifractal analysis in metric spaces." Nonlinearity 26, no. 8 (June 26, 2013): 2157–73. http://dx.doi.org/10.1088/0951-7715/26/8/2157.

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50

SEARSTON, IAN. "NONLINEAR ANALYSIS IN GEODESIC METRIC SPACES." Bulletin of the Australian Mathematical Society 92, no. 3 (August 5, 2015): 514–15. http://dx.doi.org/10.1017/s0004972715000854.

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