Fixed point results in controlled revised fuzzy metric spaces with an application to the transformation of solar energy to electric powe
Abstract
Introduction/purpose: This study establishes sufficient conditions for a sequence to be Cauchy within the framework of controlled revised fuzzy metric spaces. It also generalizes the concept of Banach’s contraction principle by introducing several new contraction conditions. The aim is to derive various fixed-point results that enhance the understanding of these mathematical structures.
Methods: The researchers employ rigorous mathematical techniques to develop their findings. By defining a set of novel contraction mappings and utilizing properties of controlled revised fuzzy metric spaces, they analyze the implications for sequence convergence. The methodology includes constructing specific examples to illustrate the theoretical results.
Results: The study presents several fixed-point theorems derived from the generalized contraction conditions. Additionally, it provides a number of non-trivial examples that substantiate the claims and demonstrate the applicability of the results in practical scenarios. A significant application is explored regarding the conversion of solar energy into electric power, utilizing differential equations to highlight this connection.
Conclusion: The findings deepen the understanding of Cauchy sequences in fuzzy metric spaces and offer a broader perspective on the application of the fixed-point theory in real-world scenarios. The results pave the way for further research in both theoretical mathematics and its practical applications, particularly in the field of renewable energy.
References
Adabitabar Firozja, A. & Firouzian, S. 2015. Definition of fuzzy metric space with t-conorm. Annals of Fuzzy Mathematics and Informatics, 10(4), pp.649-655 [online]. Available at: http://www.afmi.or.kr [Accessed: 02 February 2024].
Al-Khaleel, M., Al-Sharif, S. & AlAhmad, R. 2023. On Cyclic Contractive Mappings of Kannan and Chatterjea Type in Generalized Metric Spaces. Mathematics, 11(4), art.number:890. Available at: https://doi.org/10.3390/math11040890.
Branga, A.N. & Olaru, I.M. 2022. Generalized Contractions and Fixed Point Results in Spaces with Altering Metrics. Mathematics, 10(21), art.number:4083. Available at: https://doi.org/10.3390/math10214083.
Czerwik, S. 1993. Contraction mappings in b-metricspaces. Acta Mathematica et Informatica Universitatis Ostraviensis, 1(1), pp.5-11 [online]. Available at: https://dml.cz/handle/10338.dmlcz/120469 [Accessed: 02 February 2024].
George, A. & Veeramani, P. 1994. On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64(3), pp.395-399. Available at: https://doi.org/10.1016/0165-0114(94)90162-7.
Gregori, V. & Miñana, J.-J. 2021. A Banach contraction principle in fuzzy metric spaces defined by means of t-conorms. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 115, art.number:129. Available at: https://doi.org/10.1007/s13398-021-01068-6.
Grigorenko, O., Miñana, J.J., Šostak, A. & Valero, O. 2020. On t-Conorm Based Fuzzy (Pseudo)metrics. Axioms, 9(3), art.number:78. Available at: https://doi.org/10.3390/axioms9030078.
Hadžić, O. 1979. A fixed point theorem in Menger spaces. Publications De L’institute Mathématique, Nouvelle serie, 20(40), pp.107-112 [online]. Available at: http://elib.mi.sanu.ac.rs/files/journals/publ/46/17.pdf [Accessed: 02 February 2024].
Hadžić, O. & Pap, E. 2001. Probabilistic metric spaces. In: Fixed Point Theory in Probabilistic Metric Spaces. Mathematics and Its Applications, 536, pp.47-94. Dordrecht: Springer. Available at: https://doi.org/10.1007/978-94-017-1560-7_2.
Hassanzadeh, Z. & Sedghi, S. 2018. Relation betweenb-metric and fuzzy metric spaces. Mathematica Moravica, 22(1), pp.55-63. Available at: https://doi.org/10.5937/MatMor1801055H.
Heilpern, S. 1981. Fuzzy mappings and fixed point theorem. Journal of Mathematical Analysis and Applications, 81(2), pp.566-569. Available at: https://doi.org/10.1016/0022-247X(81)90141-4.
Hussain, A., Ishtiaq, U., Ahmed, K. & Al-Sulami, H. 2022. On Pentagonal Controlled Fuzzy Metric Spaces with an Application to Dynamic Market Equilibrium. Journal of Function Spaces, 2022(1), art.number: 5301293. Available at: https://doi.org/10.1155/2022/5301293.
Ishtiaq, U., Kattan, D.A., Ahmad, K., Sessa, S. & Ali, F. 2023. Fixed Point Results in Controlled Fuzzy Metric Spaces with an Application to the Transformation of Solar Energy to Electric Power. Mathematics, 11(15), art.number:3435. Available at: https://doi.org/10.3390/math11153435.
Ishtiaq, U., Saleem, N., Uddin, F., Sessa, S., Ahmad, K. & di Martino, F. 2022. Graphical Views of Intuitionistic Fuzzy Double-Controlled Metric-Like Spaces and Certain Fixed-Point Results with Application. Symmetry, 14(11), art.number:2364. Available at: https://doi.org/10.3390/sym14112364.
Kaleva, O. & Seikkala, S. 1984. On fuzzy metric spaces. Fuzzy Sets and Systems, 12(3), pp.215-229. Available at: https://doi.org/10.1016/0165-0114(84)90069-1.
Kider, J.R. 2020. Some Properties of Algebra Fuzzy Metric Space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(2), pp.43-56. Available at: https://doi.org/10.29304/jqcm.2020.12.2.695.
Kider, J.R. 2021. Application of Fixed Point in Algebra Fuzzy Normed Spaces. Journal of Physics: Conference Series, 1879, art.number:022099. Available at: https://doi.org/10.1088/1742-6596/1879/2/022099.
Klement, E.P., Mesiar, R. & Pap, E. 2004. Problems on triangular norms and related operators. Fuzzy Sets and Systems, 145(3), pp.471-479. Available at: https://doi.org/10.1016/S0165-0114(03)00303-8.
Kramosil, I. & Michálek, J. 1975. Fuzzy metrics and statistical metric spaces. Kybernetika, 11(5), pp.336-344 [online] . Available at: https://www.kybernetika.cz/content/1975/5/336 [Accessed: 19 January 2024].
Li, S.-F., He, F. & Lu, S.-M. 2022. Kaleva-Seikkala’sType Fuzzy b-Metric Spaces and Several Contraction Mappings. Journal of Function Spaces, 2022(1), art.number: 2714912. Available at: https://doi.org/10.1155/2022/2714912.
Mlaiki, N., Aydi, H., Souayah, N. & Abdeljawad, T. 2018. Controlled Metric Type Spaces and the Related Contraction Principle. Mathematics, 6(10), art.number:194. Available at: https://doi.org/10.3390/math6100194.
Moussaoui, A., Hussain, N., Melliani, S., Nasr, H. & Imdad, M. 2022. Fixed point results via extended FZ-simulation functions in fuzzy metric spaces. Journal of Inequalities and Applications, art.number:69. Available at: https://doi.org/10.1186/s13660-022-02806-z.
Muraliraj, A. & Thangathamizh, R. 2021a. Fixed point theorems in revised fuzzy metric space. Advances in Fuzzy Sets and Systems, 26(2), pp.103-115. Available at: https://doi.org/10.17654/FS026020103.
Muraliraj, A. & Thangathamizh, R. 2021b. Introduction on Revised fuzzy modular spaces. Global Journal of Pure and Applied Mathematics, 17(2), pp.303-317. Available at: https://doi.org/10.37622/GJPAM/17.2.2021.303-317.
Muraliraj, A. & Thangathamizh, R. 2022. Relation-Theoretic Revised Fuzzy Banach Contraction Principle and Revised Fuzzy Eldestein Contraction Theorem. JMSCM Journal of Mathematical Sciences & Computational Mathematics, 3(2), pp.197-207. Available at: https://doi.org/10.15864/jmscm.3205.
Muraliraj, A. & Thangathamizh, R. 2023. Some topological properties of revised fuzzy cone metric spaces. Ratio Mathematica, 47, pp.42-51. Available at: https://doi.org/10.23755/rm.v47i0.734.
Muraliraj, A., Thangathamizh, R., Popovic, N., Savic, A. & Radenovic, S. 2023. The First Rational Type Revisd Fuzzy-Contractions in Revisd Fuzzy Metric Spaces with an Applications. Mathematics, 11(10), art.number:2244. Available at: Available at: https://doi.org/10.3390/math11102244.
Rakić, D., Mukheimer, A., Došenović, T., Mitrović, Z. & Radenović, S. 2020. On some new fixed point results in fuzzy b-metric spaces”. Journal of Inequalities and Applications, art.number:99. Available at: https://doi.org/10.1186/s13660-020-02371-3.
Sedghi, S. & Shobe, N. 2012. Common fixed point theorem in b-fuzzy metric space. Nonlinear Functional Analysis and Applications (NFAA), 17(3), pp.349-359 [online]. Available at: http://nfaa.kyungnam.ac.kr/journal-nfaa/index.php/NFAA/article/view/38 [Accessed: 02 February 2024].
Sedghi, S. & Shobkolaei, N. 2014. Common fixed point theorem for R-weakly commuting maps in b-fuzzy metric spaces. Nonlinear Functional Analysis and Applications (NFAA), 19(2) pp.285-295 [online]. Available at: http://nfaa.kyungnam.ac.kr/journal-nfaa/index.php/NFAA/article/view/238 [Accessed: 02 February 2024].
Sezen, M.S. 2021. Controlled fuzzy metric spaces and some related fixed point results. Numerical Methods for Partial Differential Equations, 37(1), pp.583-593. Available at: https://doi.org/10.1002/num.22541.
Schweizer, B. & Sklar, A. 1960. Statistical metric spaces. Pacific Journal of Mathematics, 10(1), pp.313-334. Available at: https://doi.org/10.2140/pjm.1960.10.313.
Šostak, A. 2018. George-Veeramani Fuzzy Metrics Revised. Axioms, 7(3), art.numner:60. Available at: https://doi.org/10.3390/axioms7030060.
Thangathamizh, R., Muraliraj, A. & Shanmugavel, P. 2024. New approach of Lebesgue integral in revised fuzzy cone metric spaces via unique coupled fixed point theorems. Vojnotehnički glasnik/Military Technical Courier, 72(3), pp.1029-1045. Available at: https://doi.org/10.5937/vojtehg72-48816.
Younis, M., Singh, D. & Abdou, A.A.N. 2022. A fixed point approach for tuning circuit problem in dislocated b-metric spaces. Mathematical Methods in the Applied Science, 45(4), pp.2234-2253. Available at: https://doi.org/10.1002/mma.7922.
Zadeh, L.A. 1965. Fuzzy Sets. Information and Control, 8(3), pp.338-353. Available at: https://doi.org/10.1016/S0019-9958(65)90241-X.
Copyright (c) 2024 Ravichandran Thangathamizh, Abdelhamid Moussaoui, Tatjana Došenović, Stojan Radenović
This work is licensed under a Creative Commons Attribution 4.0 International License.
Proposed Creative Commons Copyright Notices
Proposed Policy for Military Technical Courier (Journals That Offer Open Access)
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).