On Some Properties in Fuzzy Metric Space
DOI:
https://doi.org/10.29304/jqcm.2021.13.1.745Keywords:
Fuzzy closed ball, , Fuzzy convergent sequence, Fuzzy metric space, Fuzzy open ballAbstract
Fuzzy metric spaces theory has an essential significance in mathematics, statistics, computer science, etc. In this paper, several basic properties of the fuzzy metric space (FM-space) ( ) are discussed. The concepts of fuzzy convergent sequence, fuzzy Cauchy sequence, fuzzy open ball and fuzzy closed ball are recalled, then main theorems related to these concepts are proved.
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References
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[38] A. AUKŠTUOLIS, M. Girtan, G. A. Mousdis, R. Mallet, M. Socol, and M. Rasheed, "A. Stanculescu, Measurement of charge carrier mobility in perovskite nanowire films by photo-CELIV method", Proceedings of the Romanian Academy Series a-Mathematics Physics Technical Sciences Information Science, vol. 18 (1), (2017), pp. 34-41.
[39] D. Bouras, A. Mecif, R. Barillé, A. Harabi, M. Rasheed, A. Mahdjoub, and M. Zaabat, "Cu: ZnO deposited on porous ceramic substrates by a simple thermal method for photocatalytic application", Ceramics International, vol. 44 (17), (2018), pp. 21546-21555.
[40] E. Kadri, K. Dhahri, A. Zaafouri, M. Krichen, M. Rasheed, K. Khirouni, and R. Barillé, "Ac conductivity and dielectric behavior of a−Si:H/c− Si1−yGey/p−Si thin films synthesized by molecular beam epitaxial method", Journal of Alloys and Compounds, vol. 705, (2017), pp. 708-713.
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[45] F. Dkhilalli, S. M. Borchani, M. Rasheed, R. Barille, K. Guidara, and M. Megdiche, "Structural, dielectric, and optical properties of the zinc tungstate ZnWO4 compound", Journal of Materials Science: Materials in Electronics, vol. 29 (8), (2018), pp. 6297-6307.
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[47] F. Dkhilalli, S. Megdiche, K. Guidara, M. Rasheed, R. Barillé, and M. Megdiche, "AC conductivity evolution in bulk and grain boundary response of sodium tungstate Na2WO4", Ionics, vol. 24 (1), (2018), pp. 169-180.
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[49] M. Enneffati, B. Louati, K. Guidara, M. Rasheed, and R. Barillé, "Crystal structure characterization and AC electrical conduction behavior of sodium cadmium orthophosphate", Journal of Materials Science: Materials in Electronics, vol. 29 (1), (2018), pp. 171-179.
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[73] M. RASHEED, Osama Alabdali, S. SHIHAB and T. RASHID, "Evaluation and Determination of the Parameters of a Photovoltaic Cell by an Iterative Method", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 34-42.
[74] M. N. Mohammedali, M. RASHEED, S. SHIHAB and T. RASHID, "Optimal Parameters Estimation of Silicon Solar Cell Using Fuzzy Logic: Analytical Method", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp.55-61.
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[77] M. A. Sarhan, S. SHIHAB, M. RASHEED, "A novel Spectral Modified Pell Algorithm for Solving Singular Differential Equations", Al- Mustansiriyah Journal of Science, vol. 32, (1), (2021), In press.
[2] Zadeh L. Fuzzy sets. Information and Control. 1965; 8(3): 338-353.
[3] Kramosil D, Michalek J. Fuzzy metric and statistical metric spaces. Kybernetika. 1975; 11: 326-334.
[4] Kaleva O, Seikkala S. On fuzzy metric spaces. Fuzzy Sets and Systems. 1984; 12(3): 215-229.
[5] Kumar MV, Subhani SM. Application of Common Fixed Point Theorem on Fuzzy Metric Space. In Proceedings of the World Congress on Engineering and Computer Science. 2017; 1.
[6] Karayılan H, Telci M. Caristi type fixed point theorems in fuzzy metric Spaces. Hacet. J. Math. Stat. 2019; 48 (1): 75 – 86.
[7] Prasad B, Katiyar K. Multi Fuzzy Fractal Theorems in Fuzzy Metric Spaces. Fuzzy Inf. Eng. 2017; (9): 225-236.
[8] Tian J. Note on common fixed point theorems in fuzzy metric spaces using the CLRg property. Fuzzy Sets and Systems. 2019; 1-4.
[9] Gregori V, Miñana JJ, Morillas S, Sapena A. Cauchyness and convergence in fuzzy metric spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 2017; (111): 25–37.
[10] Gregori V, Miñana J, Miravet D. Contractive sequences in fuzzy metric spaces. Fuzzy Sets and Systems. 2019; 1-9.
[11] Mohammedali MN, Sabri RI, RASHEED M, SHIHAB S. Some Results on G-Normed Linear Space. Journal of Southwest Jiaotong University. 2020; 5(3).
[12] Sabri RI, Mohammedali MN, RASHEED M, SHIHAB S. Compactness of Soft Fuzzy Metric Space. Journal of Southwest Jiaotong University. 2020; 5(3).
[13] Raghad I, Maida N. New fuzzy metric spaces and fuzzy matrices. Journal of principal Education of AL Mustansiriyah University. 2014; 20(82): 1-6.
[14] Erwin K. Introductory functional analysis with applications. New York. John-Wily & Sons. 1978.
[15] M. A. Sarhan, "Effect of Silicon Solar Cell Physical Factors on Maximum Conversion Efficiency Theoretically and Experimentally", Insight-Electronic, vol. 1 (1), (2019), pp. 24-30.
[16] M. A. Sarhan, S. Shihab, B. E. Kashem and M. Rasheed, "New Exact Operational Shifted Pell Matrices and Their Application in Astrophysics", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[17] F. S. Tahir, and M. S. Rasheed, "Decline in the Performance of Silicon Solar Cell Parameters with the Ambient Temperature in Baghdad", Journal of the College of Basic Education, vol. 18 (75), (2012), pp. 95-111.
[18] F. S. Tahir, M. S. Rasheed, and I. A. Hameed, "Analysis the Performance of Silicon Solar Cell Parameters with the Ambient Temperature using Fuzzy Logic", Journal of the College of Basic Education, vol. 18 (75), (2012), pp. 173-183.
[19] R. Jalal, S. Shihab, M. A. Sarhan, and M. Rasheed. "Spectral Numerical Algorithm for Solving Optimal Control Using Boubaker-Turki Operational Matrices", In Journal of Physics: Conference Series, vol. 1660, no. 1, p. 012090. IOP Publishing, (2020).
[20] M. RASHEED, "Linear Programming for Solving Solar Cell Parameters", Insight-Electronic, vol. 1 (1), (2019), pp. 10-16.
[21] M. RASHEED, and M. A. Sarhan, "Solve and Implement the main Equations of Photovoltaic Cell Parameters Using Visual Studio Program", Insight-Mathematics, vol. 1 (1), (2019), pp. 17-25.
[22] M. Rasheed, and R. Barillé, "Room temperature deposition of ZnO and Al: ZnO ultrathin films on glass and PET substrates by DC sputtering technique", Optical and Quantum Electronics, vol. 49 (5), (2017), pp. 1-14.
[23] M. RASHEED, and S. SHIHAB, "Analytical Modeling of Solar Cells", Insight Electronics, vol. 1 (2), (2019), pp. 1-9.
[24] M. RASHEED, and S. SHIHAB, "Modifications to Accelerate the Iterative Algorithm for the Single Diode Model of PV Model", Iraqi Journal of Physics (IJP), vol. 18 (47), (2020), pp. 33-43.
[25] M. Rasheed, and S. Shihab, "Numerical Techniques for Solving Parameters of Solar Cell", Applied Physics, vol. 3 (1), (2020), pp. 16-27.
[26] M. RASHEED, and S. SHIHAB, "Parameters Estimation for Mathematical Model of Solar Cell", Electronics Science Technology and Application, vol. 6, (1), (2019), pp. 20-28.
[27] M. Rasheed, O. Alabdali and S. Shihab, "A New Technique for Solar Cell Parameters Estimation of The Single-Diode Model", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[28] M. Rasheed, O. Y. Mohammed, S. Shihab, and Aqeel Al-Adili, "A comparative Analysis of PV Cell Mathematical Model", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[29] M. Rasheed, O. Y. Mohammed, S. Shihab, and Aqeel Al-Adili, "Explicit Numerical Model of Solar Cells to Determine Current and Voltage", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[30] M. Rasheed, O. Y. Mohammed, S. Shihab, and Aqeel Al-Adili, "Parameters Estimation of Photovoltaic Model Using Nonlinear Algorithms", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[31] M. S. Rasheed, and S. Shihab, "Analysis of Mathematical Modeling of PV Cell with Numerical Algorithm". Advanced Energy Conversion Materials, vol. 1 (2), (2020), pp. 70-79. Available from: http://ojs.wiserpub.com/index.php/AECM/article/view/328.
[32] M. RASHEED, S. SHIHAB, T. RASHID and T. D. Ounis, "Determination of PV Model Parameters Using Bisection and Secant Methods", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13, (1), (2021), pp. 43-54.
[33] M. S. Rasheed and S. Shihab, "Modelling and Parameter Extraction of PV Cell Using Single-Diode Model". Advanced Energy Conversion Materials, 1 (2), (2020), pp. 96-104. Available from: http://ojs.wiserpub.com/index.php/AECM/article/view/550.
[34] M. S. Rasheed, "Acceleration of Predictor Corrector Halley Method in Astrophysics Application", International Journal of Emerging Technologies in Computational and Applied Sciences, vol. 1 (2), (2012), pp. 91-94.
[35] S. Shihab, M. Rasheed, O. Alabdali and A. A. Abdulrahman, "A Novel Predictor-Corrector Hally Technique for Determining The Parameters for Nonlinear Solar Cell Equation", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[36] S. SHIHAB, and M. RASHEED, "Modeling and Simulation of Solar Cell Mathematical Model Parameters Determination Based on Different Methods", Insight Mathematics, vol. 1 (1), (2019), pp. 1-16.
[37] A. A. Abdulrahman, M. RASHEED and S. SHIHAB, "The Analytic of Image Processing Smoothing Spaces Using Wavelet", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[38] A. AUKŠTUOLIS, M. Girtan, G. A. Mousdis, R. Mallet, M. Socol, and M. Rasheed, "A. Stanculescu, Measurement of charge carrier mobility in perovskite nanowire films by photo-CELIV method", Proceedings of the Romanian Academy Series a-Mathematics Physics Technical Sciences Information Science, vol. 18 (1), (2017), pp. 34-41.
[39] D. Bouras, A. Mecif, R. Barillé, A. Harabi, M. Rasheed, A. Mahdjoub, and M. Zaabat, "Cu: ZnO deposited on porous ceramic substrates by a simple thermal method for photocatalytic application", Ceramics International, vol. 44 (17), (2018), pp. 21546-21555.
[40] E. Kadri, K. Dhahri, A. Zaafouri, M. Krichen, M. Rasheed, K. Khirouni, and R. Barillé, "Ac conductivity and dielectric behavior of a−Si:H/c− Si1−yGey/p−Si thin films synthesized by molecular beam epitaxial method", Journal of Alloys and Compounds, vol. 705, (2017), pp. 708-713.
[41] E. Kadri, M. Krichen, R. Mohammed, A. Zouari, and K. Khirouni, "Electrical transport mechanisms in amorphous silicon/crystalline silicon germanium heterojunction solar cell: impact of passivation layer in conversion efficiency", Optical and Quantum Electronics, vol. 48 (12), (2016), pp. 1-15.
[42] S. H. Aziz, S. SHIHAB, M. RASHEED, "On Some Properties of Pell Polynomials", Al-Qadisiyah Journal of Pure Science, vol. 26, (1), (2020), pp. 39-54.
[43] M. A. Sarhan, S. SHIHAB, M. RASHEED, "Some Results on a Two Variables Pell Polynomials", Al-Qadisiyah Journal of Pure Science, vol. 26, (1), (2020), pp. 55-70.
[44] E. Kadri, O. Messaoudi, M. Krichen, K. Dhahri, M. Rasheed, E. Dhahri, A. Zouari, K. Khirouni, and R. Barillé, "Optical and electrical properties of SiGe/Si solar cell heterostructures: Ellipsometric study", Journal of Alloys and Compounds, vol. 721, (2017), pp. 779-783.
[45] F. Dkhilalli, S. M. Borchani, M. Rasheed, R. Barille, K. Guidara, and M. Megdiche, "Structural, dielectric, and optical properties of the zinc tungstate ZnWO4 compound", Journal of Materials Science: Materials in Electronics, vol. 29 (8), (2018), pp. 6297-6307.
[46] F. Dkhilalli, S. M. Borchani, M. Rasheed, R. Barille, S. Shihab, K. Guidara, and M. Megdiche, "Characterizations and morphology of sodium tungstate particles", Royal Society open science, vol. 5 (8), (2018), pp. 1-12.
[47] F. Dkhilalli, S. Megdiche, K. Guidara, M. Rasheed, R. Barillé, and M. Megdiche, "AC conductivity evolution in bulk and grain boundary response of sodium tungstate Na2WO4", Ionics, vol. 24 (1), (2018), pp. 169-180.
[48] K. Guergouria A. Boumezoued, R. Barille, D. Rechemc, M. Rasheed, and M. Zaabata, "ZnO nanopowders doped with bismuth oxide, from synthesis to electrical application", Journal of Alloys and Compounds, vol. 791, (2019), pp. 550-558.
[49] M. Enneffati, B. Louati, K. Guidara, M. Rasheed, and R. Barillé, "Crystal structure characterization and AC electrical conduction behavior of sodium cadmium orthophosphate", Journal of Materials Science: Materials in Electronics, vol. 29 (1), (2018), pp. 171-179.
[50] M. Enneffati, M. Rasheed, B. Louati, K. Guidara, and R. Barillé, "Morphology, UV–visible and ellipsometric studies of sodium lithium orthovanadate", Optical and Quantum Electronics, vol. 51 (9), (2019), vol. 299.
[51] M. Enneffati, M. Rasheed, B. Louatia, K. Guidaraa, S. Shihab, and R. Barillé, "Investigation of structural, morphology, optical properties and electrical transport conduction of Li0.25Na0.75CdVO4 compound", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[52] M. M. Abbas and M. Rasheed, "Solid State Reaction Synthesis and Characterization of Cu doped TiO2 Nanomaterials", In Journal of Physics: Conference Series, IOP Publishing, (2021), in press.
[53] M. M. Abbas and M. RASHEED, "Investigation of structural, Mechanical, Thermal and Optical Properties of Cu Doped TiO2", Iraqi Journal of Physics (IJP), (2020), in press.
[54] M. Rasheed, and R. Barillé, "Comparison the optical properties for Bi2O3 and NiO ultrathin films deposited on different substrates by DC sputtering technique for transparent electronics", Journal of Alloys and Compounds, vol. 728, (2017), pp. 1186-1198.
[55] M. Rasheed, and Régis Barillé, "Optical constants of DC sputtering derived ITO, TiO2 and TiO2: Nb thin films characterized by spectrophotometry and spectroscopic ellipsometry for optoelectronic devices", Journal of Non-Crystalline Solids, vol. 476, (2017), pp. 1-14.
[56] M. RASHEED, S. SHIHAB and T. RASHID, "Parameters Determination of PV Cell Using Computation Methods", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 1-9.
[57] M. Rasheed, S. Shihab, O. Alabdali and H. H. Hussein, "Parameters Extraction of a Single-Diode Model of Photovoltaic Cell Using False Position Iterative Method", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[58] M. RASHEED, S. SHIHAB, and O. W. Sabah, "An investigation of the Structural, Electrical and Optical Properties of Graphene-Oxide Thin Films Using Different Solvents", In Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[59] N. B. Azaza, S. Elleuch, M. Rasheed, D. Gindre, S. Abid, R. Barille, Y. Abid, and H. Ammar, "3-(p-nitrophenyl) Coumarin derivatives: Synthesis, linear and nonlinear optical properties", Optical Materials, vol. 96, (2019), pp. 109328.
[60] T. Saidani, M. Zaabat, M. S. Aida, R. Barille, M. Rasheed, and Y. Almohamed, "Influence of precursor source on sol–gel deposited ZnO thin films properties", Journal of Materials Science: Materials in Electronics, vol. 28 (13), (2017), pp. 9252-9257.
[61] W. Saidi, N. Hfaidh, M. Rasheed, M. Girtan, A. Megriche, and M. EL Maaoui, "Effect of B2O3 addition on optical and structural properties of TiO2 as a new blocking layer for multiple dye sensitive solar cell application (DSSC)", RSC Advances, vol. 6 (73), (2016), pp. 68819-68826.
[62] M. RASHEED, "Investigation of Solar Cell Factors using Fuzzy Set Technique", Insight-Electronic, vol. 1 (1), (2019), pp. 17-23.
[63] M. Rasheed, and M. A. Sarhan, "Characteristics of Solar Cell Outdoor Measurements Using Fuzzy Logic Method", Insight-Mathematics, vol. 1 (1), (2019), pp. 1-8.
[64] M. RASHEED, S. SHIHAB, T. RASHID, "Two Step and Newton- Raphson Algorithms in the Extraction for the Parameters of Solar Cell", Al-Qadisiyah Journal of Pure Science, (2021), in press.
[65] M. RASHEED, and M. A. Sarhan, "Measuring the Solar Cell Parameters Using Fuzzy Set Technique", Insight-Electronic, vol. 1 (1), (2019), pp. 1-9.
[66] M. S. Rasheed, "An Improved Algorithm For The Solution of Kepler‘s Equation For An Elliptical Orbit", Engineering & Technology Journal, vol. 28 (7), (2010), pp. 1316-1320.
[67] M. S. Rasheed, "Approximate Solutions of Barker Equation in Parabolic Orbits", Engineering & Technology Journal, vol. 28 (3), (2010), pp. 492-499.
[68] M. S. Rasheed, "Comparison of Starting Values for Implicit Iterative Solutions to Hyperbolic Orbits Equation", International Journal of Software and Web Sciences (IJSWS), vol. 1 (2), (2013), pp. 65-71.
[69] M. S. Rasheed, "Fast Procedure for Solving Two-Body Problem in Celestial Mechanic", International Journal of Engineering, Business and Enterprise Applications, vol. 1 (2), (2012), pp. 60-63.
[70] M. S. Rasheed, "Modification of Three Order Methods for Solving Satellite Orbital Equation in Elliptical Motion", Journal of university of Anbar for Pure science, vol. 14 (1), (2020), pp. 33-37.
[71] M. S. Rasheed, "On Solving Hyperbolic Trajectory Using New Predictor-Corrector Quadrature Algorithms", Baghdad Science Journal, vol. 11 (1), (2014), pp. 186-192.
[72] M. S. Rasheed, "Solve the Position to Time Equation for an Object Travelling on a Parabolic Orbit in Celestial Mechanics", DIYALA JOURNAL FOR PURE SCIENCES, vol. 9 (4), (2013), pp. 31-38.
[73] M. RASHEED, Osama Alabdali, S. SHIHAB and T. RASHID, "Evaluation and Determination of the Parameters of a Photovoltaic Cell by an Iterative Method", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 34-42.
[74] M. N. Mohammedali, M. RASHEED, S. SHIHAB and T. RASHID, "Optimal Parameters Estimation of Silicon Solar Cell Using Fuzzy Logic: Analytical Method", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp.55-61.
[75] M. N. Mohammedali, M. RASHEED, S. SHIHAB and T. RASHID, "Fuzzy Set Technique Application: The Solar Cell", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 62-69.
[76] R. J. Mitlif, M. RASHEED, S. SHIHAB and T. RASHID, "Linear Programming Method Application in a Solar Cell", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 10-21.
[77] M. A. Sarhan, S. SHIHAB, M. RASHEED, "A novel Spectral Modified Pell Algorithm for Solving Singular Differential Equations", Al- Mustansiriyah Journal of Science, vol. 32, (1), (2021), In press.
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Published
2021-01-23
How to Cite
Sabri, R. I., RASHEED, M., Alabdali, O., SHIHAB, S., & RASHID, T. (2021). On Some Properties in Fuzzy Metric Space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(1), Math Page 55– 61. https://doi.org/10.29304/jqcm.2021.13.1.745
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Math Articles
