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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Wireless sensor networks with modular metric spaces

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pp. 659–667Vol. 28Issue 2March 2025DOI: 10.47974/JIM-2109XML
Received:
13 Feb 2024
Published Online:
15 Mar 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2109
Pages:
659–667

Abstract

Chistyakov introduced notions of Metric Modular Spaces (MMS) recently. There are motivating chances when integrating the Fixed-Point Theorem (FPT) of MMS into the model and function of a Wireless Sensor Network (WSN), particularly when it comes to reformation network functions, routing algorithms, and data aggregation methods. In WSN data communication, security is a dynamic problem. Dynamic routing algorithms improve data security without requiring any added information by finding the shortest path for data transmission between two connected data packets. Applications requiring remote environmental condition monitoring are increasingly using WSN. Specifically, dense WSNs are evolving as a critical detecting stage for the Internet of Things (IoT). WSN can form the raw data, and to assure effective data transfer, a network model and effective node direction are required. Data aggregation is a method used by WSN to design a data fusion policy, and minimum data is transmitted inside the network. The study’s objective is the existence and uniqueness of FPT in MMS via integral type contraction. Also, the iteration of Fixed Points (FP) of Contracts in Settings in MMS was studied in this paper.

Keywords

Subject Classifications

47H1054H25

References

[1] L. Karim and M. S. Al-kahtani, “Sensor data aggregation in a multi-layer big data framework,” in 2016 IEEE 7th Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON), IEEE, pp. 1–7 (2016).
[2] S. Banach, “Sur les opérations dans les ensembles abstraits et leurs applications aux equations integrales,” Fundam. Math., vol. 3, pp. 133-181 (1922).
[3] V. V. Chistyakov, “Modular metric spaces, I: Basic concepts,” Nonlinear Anal., vol. 72, pp. 1–14 (2010).
[4] V. V. Chistyakov, “A fixed point theorem for contractions in modular metric spaces,” e-Print, arXiv:1112.5561, pp. 1–31 (2011).
[5] V. V. Chistyakov, Metric Modular Spaces, Theory and Applications, Springer International Publishing, Switzerland (2015).
[6] A. Aftabizadeh, Y. Huang, and N. Pavel, “Nonlinear third-order differential equations with anti-periodic boundary conditions and some optimal control problems,” J. Math. Anal. Appl., vol. 192, pp. 266-293 (1995).
[7] A. Branciari, “A fixed point theorem for mappings satisfying a general contractive condition of integral type,” Int. J. Math. Math. Sci., vol. 29, no. 9, pp. 531-536 (2002).
[8] H. Nakano, Modulared Semi-Ordered Linear Spaces, in Tokyo Math. Book Ser., vol. 1, Maruzen Co., Tokyo (1950).
[9] S. Siddamsetti, H. Z. Almngoshi, K. Dinesh, G. C. Prashant, M. A. Bennet, P. Dadheech, and S. Sengan, “Modular metric spaces: Some fixed-point theorems and application of secure dynamic routing for WSN,” J. Interdiscip. Math., vol. 27, no. 2, pp. 393-401 (2024), DOI: 10.47974/JIM-1890.
[10] H. M. A. Ghanimi, T. Gopalakrishnan, G. J. S. Deol, K. Amarendra, P. Dadheech, and S. Sengan, “Chebyshev polynomial approximation in CNN for zero-knowledge encrypted data analysis,” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 2-A, pp. 203–214 (2024), DOI: 10.47974/JDMSC-1880.
[11] H. M. A. Ghanimi, R. P. Melgarejo-Bolivar, A. Tumi-Figueroa, S. Ray, P. Dadheech, and S. Sengan, “Merkle-Damg hash functions and blockchains: Securing electronic health records,” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 2-A, pp. 237–248 (2024), DOI: 10.47974/JDMSC-1878.
[12] P. V. Sagar, H. M. A. Ghanimi, L. A. J. Prabhu, L. Raja, P. Dadheech, and S. Sengan, “Secure multi-party computation in deep learning: Enhancing privacy in distributed neural networks,” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 2-A, pp. 249–259 (2024), DOI: 10.47974/JDMSC-1879.
[13] G. R. K. Rao, H. M. A. Ghanimi, V. Ramachandran, D. Al-Qahtani, P. Dadheech, and S. Sengan, “Enhanced security in federated learning by integrating homomorphic encryption for privacy-protected, collaborative model training,” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 2-A, pp. 361–370 (2024), DOI: 10.47974/JDMSC-1891.
[14] R. J. Krishna, T. Gopalakrishnan, M. Divyapushpalakshmi, K. Amarendra, P. Dadheech, and S. Sengan, “Security and privacy concerns in social networks: A mathematically modified metaheuristic-based approach,” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 2-A, pp. 371–382 (2024), DOI: 10.47974/JDMSC-1892.
[15] S. H. Nowfal, G. R. K. Rao, V. Velmurugan, S. Sengan, R. K. Bommisetti, and P. Dadheech, “Advancing viscoelastic material modeling: Tackling time-dependent behavior with fractional calculus,” J. Interdiscip. Math., vol. 27, no. 2, pp. 307–316 (2024), DOI: 10.47974/JIM-1827.
[16] P. V. Sagar, M. Rajyalaxmi, A. V. V. S. Subbalakshmi, S. Sengan, R. K. Bommisetti, and P. Dadheech, “Utilizing stochastic differential equations and random forest for precision forecasting in stock market dynamics,” J. Interdiscip. Math., vol. 27, no. 2, pp. 285–298 (2024), DOI: 10.47974/JIM-1822.

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