Some fixed point theorems via γ-ψS -contractions on S-metric spaces
Abstract
In this paper, the authors introduce generalized contractive conditions on $%
S $-metric spaces, aiming to expand the existing theory of fixed points in
such spaces. They apply these new contractive conditions to prove several
fixed-point theorems, including integral-type fixed-point results.
Additionally, they employ a geometric approach to derive new fixed-circle
theorems on $S$-metric spaces, providing necessary examples to illustrate
these results. In the concluding section, the paper highlights the
significance of these findings, particularly in the context of activation
functions, emphasizing the potential applications of their work in areas
like computational mathematics and neural networks.
References
Bimol, T., Priyobarta, N., Rohen, Y., & Singh, KA. 2024. Fixed points for Scontractions of type E on S-metric spaces. Nonlinear Functional Analysis and Applications, 29(3), pp.635-648. Available at: https://doi.org/10.22771/nfaa.2024.29.03.02
Branciari, A. 2002. A fixed point theorem for mappings satisfying a general contractive condition of integral type. International Journal of Mathematics and Mathematical Sciences, 29 (9), pp.531-536. Available at: https://onlinelibrary.wiley.com/doi/pdf/10.1155/S0161171202007524
Fetouci, N., & Radenovic, S. 2009. Some remarks and corrections of recent results from the framework of S-metric spaces. Journal of Siberian Federal University. Mathematics & Physics, 2(3), pp.258-270.
Hieu, N T., Ly, NT. & Dung, NV. 2015. A generalization of Ciric quasicontractions for maps on S-metric spaces. Thai Journal of Mathematics, 13 (2), pp.369-380. Available at: https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/515
Iqbal, M., Batool, A., Hussain, A., & Alsulami, H. 2024. Fuzzy Fixed Point Theorems in S-Metric Spaces: Applications to Navigation and Control Systems. Axioms, 13(9), pp.650. Available at: https://doi.org/10.3390/axioms13090650
Mlaiki, N., Çelik, U., Taş, N., Özgür, NY. & Mukheimer, A. 2018. Wardowski type contractions and the fixed-circle problem on S-metric spaces. Journal of Mathematics, 9. Available at: https://doi.org/10.1155/2018/9127486
Nair, V. & Hinton, GE. 2010. Rectified linear units improve restricted boltzmann machines, In 27th International Conference on Machine Learning, ICML’10, Haifa, Israel on June 21-24, 2010, pp.807-814. ISBN: 978-1-60558-907-7
Özgür, NY. & Taş, N. 2017. Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25). Mathematical Sciences, 11(1), pp.7-16. Available at: https://doi.org/10.1007/s40096-016-0199-4
Özgür, NY. & Taş, N. 2019. Some fixed-circle theorems on metric spaces. Bulletin of the Malaysian Mathematical Sciences Society , 42(4), pp.1433-1449. Available at: https://doi.org/10.1007/s40840-017-0555-z
Özgür, NY. & Taş, N. 2019. Fixed-circle problem on S-metric spaces with a geometric viewpoint. Facta Universitatis, Series: Mathematics and Informatics , 34(3), pp. 459-472. Available at: https://doi.org/10.22190/FUMI1903459O
Raji, M., Rajpoot, AK., Al-omeri, WF., Rathour, L., Mishra, LN. & Mishra, VN. 2024. Generalized α-ψ contractive type mappings and related fixed point theorems with applications. Tuijin Jishu/Journal of Propulsion Technology, 45(10), pp.5235-5246. Available at: https://www.propulsiontechjournal.com/index.php/journal/article/view/5543/3766
Samet, B., Vetro, C., Vetro, P. 2012. Fixed point theorem for contractive type mappings. Nonlinear Analysis: Theory, Methods & Applications, 75, pp.2154-2165. Available at: https://doi.org/10.1016/j.na.2011.10.014
Sedghi, S., Shobe, N. & Aliouche, A. 2012. A generalization of fixed point theorems in S-metric spaces. Matematički Vesnik, 64(3), pp.258-266. Available at: https://www.emis.de/journals/MV/123/mv12309.pdf
Sedghi, S., & Van Dung, N. 2014. Fixed point theorems on S-metric spaces. Matematički Vesnik, 255, pp.113-124. Available at: https://www.emis.de/journals/MV/141/mv14112.pdf
Copyright (c) 2025 Nihal Tas, Elif Kaplan
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).