Volume 26 • Issue 3 • PP: 105-131 • 2025
Application of Neutrosophic Pentagonal Controlled Metric Space via Orthogonality in Traffic Flow Network Using Integral Equation
Open Access & Copyright
© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF Abstract
In this paper, we researched and confirmed some of the axioms of NOPCMS (Neutrosophic orthogonal pentagonal controlled metric space). We used NOPCMS to translate the Banach contraction principle in the formerly defined spaces. Several cases were numerically evaluated, and certain findings were supported, in or- der to review what we found. Furthermore, by demonstrating their existence with a unique and comprehensive solution, we deliver proof of usage and implementation.
Keywords
References
[1] Abdeljawad. T, Mlaiki. N, Aydi. H, and Souayah. N, “Double controlled metric type spaces and some fixed point results” Mathematics, vol. 6, no. 12, p. 320, 2018.
[2] Bakhtin. I.A, “Te contraction mapping principle in quasi metric spaces”, Funct. Anal. Unianowsk Gos. Ped. Inst.vol. 30, pp. 26–37, 1989.
[3] Abdul Manna, Rahman. R, Halima Akter and Nazmun Nahar, A Study of Banach Fixed Point Theorem and It’s Applications, American Journal of Computational Mathematics, 11(02): 157–174.
[4] Czerwik. S, “Contraction mappings in b–metric spaces” Acta Mathematica Et Informatica Universitatis Ostraviensis, vol. 1, pp. 5–11, 1993.
[5] Deng. Z, “Fuzzy pseudo–metric spaces” Journal of Mathematical Analysis and Applications, vol. 86, no.
1, pp. 74–95, 1982.
[6] Eshaghi. M, Ramezani. M, Sen. M.D.L, and Cho. Y.J, “On orthogonal sets and Banach’s fixed point theorem”, Fixed Point Teory, vol. 18, pp. 569–578, 2017.
[7] Fahim Uddin, Khalil Javed, Hassen Aydi, Umar Ishtiaq and Muhammad Arshad, Control Fuzzy Metric Spaces via Orthogonality with an Application, Hindawi Journal of Mathematics, Volume 2021, 12 pages.
[8] Grabiec. M, Fixed points in fuzzy metric spaces, Fuzzy sets and systems, 27(3), 1988, pp.385–389.
[9] Jeyaraman. M and Shakila V.B, Common Fixed Point Theorems For A–Admissible Mappings In Neu- trosophic Metric Spaces, Advances And Applications In Mathematical Sciences Volume 21, Issue 4, February 2022,2069–2082.
[10] S. S. Gupta, T. K. Pandey, V. P. Raju, R. Shrivastava, R. Pandey, A. Nigam, and V. Roy, ”Diabetes estimation through data mining using optimization, clustering, and secure cloud storage strategies,” SN Computer Science, vol. 5, no. 781, 2024.
[11] Kramosil. I and Michalek. J,Fuzzy metrics and statistical metric spaces, Kybernetika, 11(5), 1975, pp.336–344.
[12] Mlaiki. N, Aydi. H, Souayah. N, and Abdeljawad. T, “Controlled metric type spaces and the related contraction principle” Mathematics, vol. 6, no. 10, p. 194, 2018.
[13] Park. J.H, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22(5), 2004, pp.1039–1046.
[14] K. D. Singh, ”Particle Swarm Optimization assisted Support Vector Machine based diagnostic system for dengue prediction at the early stage,” in Proceedings of the 3rd International Conference on Advances in Computing, Communication Control and Networking (ICAC3N), 2021, pp. 844–848.
[15] Schweizer. B and Sklar. A, Statistical metric spaces, Pacific J. Math, 10(1), 1960, pp.313–334.
[16] Sezen. M.S, Controlled Fuzzy Metric Spaces and Some Related Fixed Point Results, Wiley, Hoboken, NJ, USA, 2020.
[17] Sowndrarajan. S, Jeyaraman. M, and Florentin Smarandache, “Fixed Point Results for Contraction The- orems in Neutrosophic Metric Spaces”, Neutrosophic Sets and Systems 36, 1 (2020).
[18] Umar Ishtiaq, Salha Alshaikey, Muhammad Bilal Riaz and Khaleel Ahmad, Fixed point results in intuitionistic fuzzy pentagonal controlled metris spaces with applications to dynamic market equilibrium and satellite web coupling, Plos One, 19(8): e0303141.
[19] Zadeh. L.A, “Fuzzy sets”, Information and Control, vol. 8, no. 3, pp. 338–353, 1965.
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.