On the Stability of Soft Fixed Point in Soft Topological
Space

Samer Adnan Jubair; Mohammed H. O. Ajam

doi:https://doi.org/10.14445/22315373/IJMTT-V69I10P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 10 | Year 2023 | Article Id. IJMTT-V69I10P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I10P505

On the Stability of Soft Fixed Point in Soft Topological Space

Samer Adnan Jubair, Mohammed H. O. Ajam

Received	Revised	Accepted	Published
24 Aug 2023	29 Sep 2023	18 Oct 2023	31 Oct 2023

Citation :

Samer Adnan Jubair, Mohammed H. O. Ajam, "On the Stability of Soft Fixed Point in Soft Topological Space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 10, pp. 31-38, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I10P505

Abstract

This paper introduces stable and strongly sable of soft fixed point and studied some of their properties. The notations of converge of sequence and discrete dynamical system are generalized using soft sets. As a continuation of this, the concept of orbit was discussed to investigate the behavior of soft point under soft mapping. Also, many basic properties of these notations was presented. In addition, the concepts associated to soft points have been used to characterize soft open sets. Moreover, using some of topological properties to obtain a results concerning with soft fixed points. In particular the uniqueness of soft fixed point have been provided, which is guaranteed to exist.

Keywords

Converge of soft sequence, Discrete dynamical system, Soft fixed point, Soft set, Soft orbit.

References

[1] D. Molodtsov, “Soft Set Theory First Results,” Computers & Mathematics with Applications, vol. 37, no. 4-5, pp. 19-31, 1999.
[CrossRef] [Google Scholar] [Publisher Link]
[2] P.K. Maji, R. Biswas, and A.R. Roy, “Soft Set Theory,” Computers & Mathematics with Applications, vol. 45, no. 4-5, pp. 555- 562, 2003.
[CrossRef] [Google Scholar] [Publisher Link]
[3] Muhammad Shabir, and Munazza Naz, “On Soft Topological Spaces,” Computers & Mathematics with Applications, vol. 61, no. 7, pp. 1786-1799, 2011.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Dariusz Wardowski, “On a Soft Mapping and Its Fixed Points,” Fixed Point Theory and Applications, vol. 182, pp. 22-45, 2013.
[CrossRef] [Google Scholar] [Publisher Link]
[5] Samer Adnan Jubair, “On Soft Function in Soft Topological Spaces,” M.Sc. Thesis, University of Al -Qadisiyah, 2016.
[6] Samer Adnan Jubair, “Cancellation and Weak Cancellation S-Acts,” Al-Bahir Journal for Engineering and Pure Sciences, vol. 1, pp. 28-33, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[7] S. Nazmul, and S.K. Samanta, “Soft Topological Groups,” Kochi Journal of Mathematics, vol. 4, pp. 151–161, 2010.
[8] K.V. Babitha, and J.J. Sunil, “Soft Set Relations and Mappings,” Computers & Mathematics with Applications, vol. 60, no. 7, pp. 1840-1849, 2010.
[CrossRef] [Publisher Link]
[9] Sattar Hamzah Hameed, “On Soft Generalized Continuous Mappings,” Journal Al-Qadisiyah for Computer Science and Mathematics, vol. 1, pp. 83-92, 2016.
[Google Scholar] [Publisher Link]
[10] Sadi Bayramov, Cigdem Gunduz Aras, and Vefa Cafarli, “Soft Countable Topological Spaces,” Transactions of National Academy of Sciences of Azerbaijan. Series of Physical-Technical and Mathematical Sciences, vol. 39, no. 1, pp. 15-23, 2019.
[Publisher Link]
[11] Hu Zhao, and Fu Wenqing, “Discrete Dynamical Systems in Soft Topological Spaces,” Journal of Computational Analysis and Applications, vol. 5, pp. 867-888, 2017.
[Publisher Link]
[12] Sabir Hussain, and Bashir Ahmad, “Soft Separation Axioms in Soft Topological Spaces,” Hacettepe Journal of Mathematics and Statistics, vol. 44, no. 3, pp.559–568, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[13] I. Zorlutana et al., “Remarks on Soft Topological Spaces,” Annals of Fuzzy Mathematics and Informatics, vol. 3, no. 2, pp.171-185, 2012.
[Google Scholar] [Publisher Link]