On some fixed point results for expansive mappings in S-metric spaces
Abstract
Introduction/purpose: The aim of this paper is to establish some existence results of a fixed point for a class of expansive mappings defined on a complete S-metric space.
Methods: An iteration scheme was used.
Results: Some existing results of mappings satisfying contractive conditions are expanded to expansive ones, providing a new condition expressed in one variable under which the existence of a fixed point holds.
Conclusion: This work provides new tools to fixed point theory together with their applications.
References
Abbas, M., Hussain, A., Popović, B. & Radenović, S. 2016. Istratescu-Suzuki- Ćirić-type fixed points results in the framework of G-metric spaces. Journal of Nonlinear Sciences and Applications, 9(12), pp.6077-6095. Available at: https://doi.org/10.22436/jnsa.009.12.15.
An, T.V., Dung, N.V., Kadelburg, Z. & Radenović, S. 2015. Various generalizations of metric spaces and fixed point theorems. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 109, pp.175-198. Available at: https://doi.org/10.1007/s13398-014-0173-7.
Bakhtin, I.A. 1989. The contraction mapping principle in quasimetric spaces. Func. An., Gos. Ped. Inst. Unianowsk, 30, pp.26-37.
Dosenovic, T., Radenovic, S. & Sedghi, S. 2018. Generalized metric spaces: Survey. Turkic World Mathematical Society (TWMS) Journal of Pure and Applied Mathematics, 9(1), pp.3-17 [online]. Available at: https://www.twmsj.az/Abstract.aspx?Id=238 [Accessed: 26 April 2024].
Mohanta, S.K. 2012. Some Fixed Point Theorems on G-Expansive Mappings. Kyungpook Mathematical Journal, 52(2), pp.155-165. Available at: https://doi.org/10.5666/KMJ.2012.52.2.155.
Mojaradiafra, J. 2016. Fixed Point type Theorems in S-metric spaces. Theory of Approximation and Applications, 10(2), pp.33-41 [online]. Available at: https://sanad.iau.ir/en/Article/909865 [Accessed: 26 April 2024].
Mojaradiafra, J. & Sabbaghan, M. 2021. Some new applications of S-metric spaces by weakly compatible pairs with a limit property. The Pure and Applied Mathematics, 28(1), pp.1-13. Available at: https://doi.org/10.7468/jksmeb.2021.28.1.1.
Mojaradiafra, J., Sabbaghan, M. & Taleghan, F. 2020. Some New Fixed Point Theorems For Expansive map on S-metric spaces. Theory of Approximation and Applications, 14(2), pp.57-64 [online]. Available at: https://sanad.iau.ir/journal/msj/Article/690090?jid=690090 [Accessed: 26 April 2024].
Mustafa, Z., Awawdeh, F. & Shatanawi, W. 2010. Fixed Point Theorem for Expansive Mappings G-Metric Spaces. International Journal of Contemporary Mathematical Sciences, 5(50), pp.2463-2472 [online]. Available at: https://www.m-hikari.com/ijcms-2010/49-52-2010/mustafaIJCMS49-52-2010.pdf [Accessed: 26 April 2024].
Mustafa, Z. & Sims, B. A. 2006. New approach to generalized metric spaces. Journal of Nonlinear and Convex Analysis, 7(2), pp.289-297 [online]. Available at: http://www.yokohamapublishers.jp/online2/jncav7.html [Accessed: 26 April 2024].
Sedghi, S. & Dung, N.V. 2014. Fixed point theorems on S-metric spaces. Matematički vesnik, 66(1), pp.113-124 [online]. Available at: http://www.vesnik.math.rs/landing.php?p=mv141.cap&name=mv14112 [Ac- cessed: 25 April 2024].
Sedghi, S., Shobe, N. & Aliouche, A. 2012. A generalization of fixed point theorems in S-metric spaces. Matematički vesnik, 64(3), pp.258-266 [online]. Available at: http://www.vesnik.math.rs/landing.php?p=mv123.cap&name=mv12309 [Ac- cessed: 25 April 2024].
Vujaković, J., Mitrović, S., Mitrović, Z. & Radenović, S. 2023. On Wardowski type results within G-metric spaces. Research Gate [online]. Available at: https://www.researchgate.net/publication/366440643_On_Wardowski_type_resul ts_within_G-metric_spaces [Accessed: 26 April 2024].
Wang, S.Z., Li, B.Y., Gao, Z.M. & Iseki, K. 1984. Some fixed point theorems on expansion mappings. Mathematica Japonica, 29, pp.631-636.
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