Research article Special Issues

Common fixed point, Baire's and Cantor's theorems in neutrosophic 2-metric spaces

  • Received: 17 August 2022 Revised: 18 October 2022 Accepted: 24 October 2022 Published: 07 November 2022
  • MSC : 47H10, 54H25

  • These fundamental Theorems of classical analysis, namely Baire's Theorem and Cantor's Intersection Theorem in the context of Neutrosophic 2-metric spaces, are demonstrated in this article. Naschie discussed high energy physics in relation to the Baire's Theorem and the Cantor space in descriptive set theory. We describe, how to demonstrate the validity and uniqueness of the common fixed-point theorem for four mappings in Neutrosophic 2-metric spaces.

    Citation: Umar Ishtiaq, Khaleel Ahmad, Muhammad Imran Asjad, Farhan Ali, Fahd Jarad. Common fixed point, Baire's and Cantor's theorems in neutrosophic 2-metric spaces[J]. AIMS Mathematics, 2023, 8(2): 2532-2555. doi: 10.3934/math.2023131

    Related Papers:

  • These fundamental Theorems of classical analysis, namely Baire's Theorem and Cantor's Intersection Theorem in the context of Neutrosophic 2-metric spaces, are demonstrated in this article. Naschie discussed high energy physics in relation to the Baire's Theorem and the Cantor space in descriptive set theory. We describe, how to demonstrate the validity and uniqueness of the common fixed-point theorem for four mappings in Neutrosophic 2-metric spaces.



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    [1] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
    [2] L. C. Barros, R. C. Bassanezi, P. A. Tonelli, Fuzzy modelling in population dynamics, Ecol. Model, 128 (2000), 27–33. https://doi.org/10.1016/S0304-3800(99)00223-9 doi: 10.1016/S0304-3800(99)00223-9
    [3] A. L. Fradkov, R. J. Evans, Control of chaos: methods and applications in engineering, Chaos Solitons Fract., 29 (2005), 33–56. https://doi.org/10.1016/j.arcontrol.2005.01.001 doi: 10.1016/j.arcontrol.2005.01.001
    [4] R. Giles, A computer program for fuzzy reasoning, Fuzzy Sets Syst., 4 (1980), 221–234. https://doi.org/10.1016/0165-0114(80)90012-3 doi: 10.1016/0165-0114(80)90012-3
    [5] L. Hong, J. Q. Sun, Bifurcations of fuzzy nonlinear dynamical systems, Commun. Nonlinear Sci. Numer. Simul., 1 (2006), 1–12. https://doi.org/10.1016/j.cnsns.2004.11.001 doi: 10.1016/j.cnsns.2004.11.001
    [6] S. Barro, R. Marin, Fuzzy logic in medicine, Heidelberg: Physica-Verlag, 2002. https://doi.org/10.1007/978-3-7908-1804-8
    [7] M. S. El Naschie, On uncertainty of Cantorian geometry and two-slit experiment, Chaos Solitons Fract., 9 (1998), 517–529. https://doi.org/10.1016/S0960-0779(97)00150-1 doi: 10.1016/S0960-0779(97)00150-1
    [8] M. S. El Naschie, On the unification of heterotic strings theory and Eð 1Þ theory, Chaos Solitons Fract., 11 (2000), 2397–2408. https://doi.org/10.1016/S0960-0779(00)00108-9 doi: 10.1016/S0960-0779(00)00108-9
    [9] M. S. El Naschie, A review of E-infinity theory and the mass spectrum of high energy particle physics, Chaos Solitons Fract., 19 (2004), 209–236. https://doi.org/10.1016/S0960-0779(03)00278-9 doi: 10.1016/S0960-0779(03)00278-9
    [10] M. S. El Naschie, Quantum gravity, clifford algebras, fuzzy set theory and the fundamental constants of nature, Chaos Solitons Fract., 20 (2004), 437–450. https://doi.org/10.1016/j.chaos.2003.09.029 doi: 10.1016/j.chaos.2003.09.029
    [11] M. S. El Naschie, On two new fuzzy Kähler manifolds Klein modular space and Hooft holographic principles, Chaos Solitons Fract., 29 (2006), 876–881. https://doi.org/10.1016/j.chaos.2005.12.027 doi: 10.1016/j.chaos.2005.12.027
    [12] M. S. El Naschie, Fuzzy dodecahedron topology and E-infinity space time as a model for quantum physics, Chaos Solitons Fract., 30 (2006), 1025–1033. https://doi.org/10.1016/j.chaos.2006.05.088 doi: 10.1016/j.chaos.2006.05.088
    [13] M. S. El Naschie, A review of applications and results of E-infinity theory, Int. J. Nonlinear Sci. Numer. Simulat., 8 (2007), 11–20. https://doi.org/10.1515/IJNSNS.2007.8.1.11 doi: 10.1515/IJNSNS.2007.8.1.11
    [14] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
    [15] K. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst., 61 (1994), 137–142. https://doi.org/10.1016/0165-0114(94)90229-1 doi: 10.1016/0165-0114(94)90229-1
    [16] D. Ç oker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets Syst., 88 (1997), 81–99. https://doi.org/10.1016/S0165-0114(96)00076-0 doi: 10.1016/S0165-0114(96)00076-0
    [17] S. E. Abbas, On intuitionistic fuzzy compactness, Inform Sci., 173 (2005), 75–91. https://doi.org/10.1016/j.ins.2004.07.004 doi: 10.1016/j.ins.2004.07.004
    [18] R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fract., 27 (2006), 331–344. https://doi.org/10.1016/j.chaos.2005.03.019 doi: 10.1016/j.chaos.2005.03.019
    [19] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fract., 22 (2004), 1039–1046. https://doi.org/10.1016/j.chaos.2004.02.051 doi: 10.1016/j.chaos.2004.02.051
    [20] M. Kirişci, N. Simsek, Neutrosophic metric spaces, Math. Sci., 14 (2020), 241–248. https://doi.org/10.1007/s40096-020-00335-8 doi: 10.1007/s40096-020-00335-8
    [21] M. Mursaleen, Q. M. D. Lohani, Intuitionistic fuzzy 2-normed space and some related concepts, Chaos Solitons Fract., 42 (2009), 224–234. https://doi.org/10.1016/j.chaos.2008.11.006 doi: 10.1016/j.chaos.2008.11.006
    [22] M. Mursaleen, Q. M. D. Lohani, S. A. Mohiuddine, Intuitionistic fuzzy 2-metric space and its completion, Chaos Solitons Fract., 42 (2009), 1258–1265. https://doi.org/10.1016/j.chaos.2009.03.025 doi: 10.1016/j.chaos.2009.03.025
    [23] B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313–334. https://doi.org/10.2140/pjm.1960.10.313 doi: 10.2140/pjm.1960.10.313
    [24] S. Gähler, 2-metrische Räume und ihre topologische Struktur, Math. Nachr., 26 (1963), 115–148. https://doi.org/10.1002/mana.19630260109 doi: 10.1002/mana.19630260109
    [25] M. Mursaleen, Q. M. D. Lohani, Baire's and Cantor's theorems in intuitionistic fuzzy 2-metric spaces, Chaos Solitons Fract., 42 (2009), 2254–2259. https://doi.org/10.1016/j.chaos.2009.03.134 doi: 10.1016/j.chaos.2009.03.134
    [26] M. S. Bakry, Common fixed theorem on intuitionistic fuzzy 2-metric spaces, Mathematics, 27 (2015), 69–84.
    [27] U. Ali, H. A. Alyousef, U. Ishtiaq, K. Ahmed, S. Ali, Solving nonlinear fractional differential equations for contractive and weakly compatible mappings in neutrosophic metric spaces, J. Funct. Spaces, 2022 (2022), 1491683. https://doi.org/10.1155/2022/1491683 doi: 10.1155/2022/1491683
    [28] A. Hussain, H. Al Sulami, U. Ishtiaq, Some new aspects in the intuitionistic fuzzy and neutrosophic fixed point theory, J. Funct. Spaces, 2022 (2022), 3138740. https://doi.org/10.1155/2022/3138740 doi: 10.1155/2022/3138740
    [29] N. Saleem, I. K. Agwu, U. Ishtiaq, S. Radenović, Strong convergence theorems for a finite family of enriched strictly Pseudocontractive Mappings and Φ T-Enriched Lipschitizian Mappings using a new modified mixed-type ishikawa iteration scheme with error, Symmetry, 14 (2022), 1032. https://doi.org/10.3390/sym14051032 doi: 10.3390/sym14051032
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