The purpose of this study was to introduce soft topology generated by soft parametric metric space and prove Banach's fixed point theorem as an extension of soft complete parametric metric space. An illustrative example was given by using this fixed point theorem.
Citation: Çiğdem Aras Gündüz, Sadi Bayramov, Arzu Erdem Coşkun. Fixed point theorems of contractive mappings on soft parametric metric space[J]. AIMS Mathematics, 2024, 9(4): 7945-7954. doi: 10.3934/math.2024386
The purpose of this study was to introduce soft topology generated by soft parametric metric space and prove Banach's fixed point theorem as an extension of soft complete parametric metric space. An illustrative example was given by using this fixed point theorem.
| [1] |
M. Abbas, G. Murtaza, S. Romaguera, On the fixed point theory of soft metric spaces, Fixed Point Theory Appl., 2016 (2016), 17. https://doi.org/10.1186/s13663-016-0502-y doi: 10.1186/s13663-016-0502-y
|
| [2] | M. Abbas, Soft set theory: generalizations, fixed point theorems, and applications, España: Universitat Politecnica de Valencia, 2014. |
| [3] |
M. Aslantas, H. Sahin, D. Turkoglu, Some Caristi type fixed point theorems, J. Anal., 29 (2021), 89–103. https://doi.org/10.1007/s41478-020-00248-8 doi: 10.1007/s41478-020-00248-8
|
| [4] | M. Aslantas, H. Sahin, U. Sadullah, Some generalizations for mixed multivalued mappings, Appl. Gen. Topol., 23 (2022), 169–178. |
| [5] | S. K. Barve, Q. Kabir, M. Mohamaad, Soft fixed point theorem for contraction conditions in dislocated soft metric space, International Journal of Scientific Research and Reviews, 8 (2019), 785–791. |
| [6] | S. Bayramov, C. Gunduz, Soft locally compact spaces and soft paracompact spaces, Journal of Mathematics and System Science, 3 (2013), 122–130. |
| [7] |
R. Bhardwaj, H. G. S. Kumar, B. K. Singh, Q. A. Kabir, P. Konar, Fixed point theorems in soft parametric metric spaces, Adv. Math., 9 (2020), 1857–8365. https://doi.org/10.37418/amsj.9.12.11 doi: 10.37418/amsj.9.12.11
|
| [8] |
R. Bhardwaj, Fixed point results on a complete soft usual metric space, Turkish Journal of Computer and Mathematics Education, 11 (2020), 1035–1040. https://doi.org/10.17762/turcomat.v11i3.10220 doi: 10.17762/turcomat.v11i3.10220
|
| [9] |
C. M. Chen, Z. H. Xu, E. Karapinar, Soft fixed point theorems for the soft comparable contractions, Journal of Function Spaces, 2021 (2021), 5554510. https://doi.org/10.1155/2021/5554510 doi: 10.1155/2021/5554510
|
| [10] | S. Das, S. K. Samant, Soft real sets, soft real numbers and their properties, Journal of Fuzzy Mathematics, 20 (2012), 551–576. |
| [11] | S. Georgiev, K. Zennir, Multiple fixed-point theorems and applications in the theory of ODEs, FDEs and PDEs, 1 Eds., New York: Chapman and Hall/CRC, 2020. https://doi.org/10.1201/9781003028727 |
| [12] |
S. G. Georgiev, K. Zennir, Classical solutions for a class of IVP for nonlinear two-dimensional wave equations via new fixed point approach, Partial Differential Equations in Applied Mathematics, 2 (2020), 100014. https://doi.org/10.1016/j.padiff.2020.100014 doi: 10.1016/j.padiff.2020.100014
|
| [13] |
A. C. Guler, E. D. Yildirim, O. Ozbakir, A fixed point theorem on soft G-metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 885–894. https://doi.org/10.22436/JNSA.009.03.18 doi: 10.22436/JNSA.009.03.18
|
| [14] |
C. Aras, S. Bayramov, V. Cafarli, Fixed point theorems on soft S-metric spaces, Commun. Math. Appl., 9 (2018), 725–735. https://doi.org/10.26713/CMA.V9I4.1047 doi: 10.26713/CMA.V9I4.1047
|
| [15] |
H. Hosseinzadeh, Fixed point theorems on soft metric spaces, J. Fixed Point Theory Appl., 19 (2017), 1625–1647. https://doi.org/10.1007/s11784-016-0390-0 doi: 10.1007/s11784-016-0390-0
|
| [16] |
S. A. Khandait, R. Bhardwaj, C. Singh, Fixed point result with soft cone metric space with examples, Mathematical Theory and Modeling, 9 (2019), 62–79. https://doi.org/10.7176/MTM/9-4-07 doi: 10.7176/MTM/9-4-07
|
| [17] |
P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555–562. https://doi.org/10.1016/S0898-1221(03)00016-6 doi: 10.1016/S0898-1221(03)00016-6
|
| [18] | K. Mebarki, S. G. Georgiev, S. Djebali, K. Zennir, Fixed point theorems with applications, 1 Eds., New York: Chapman and Hall/CRC, 2023. https://doi.org/10.1201/9781003381969 |
| [19] |
D. A. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5 doi: 10.1016/S0898-1221(99)00056-5
|
| [20] |
M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786–1799. https://doi.org/10.1016/j.camwa.2011.02.006 doi: 10.1016/j.camwa.2011.02.006
|
| [21] |
S. Sonam, C. S. Chauhan, R. Bhardwaj, S. Narayan, Fixed point results in soft rectangular B-metric space, Nonlinear Functional Analysis and Applications, 28 (2023), 753–774. https://doi.org/10.22771/nfaa.2023.28.03.11 doi: 10.22771/nfaa.2023.28.03.11
|
| [22] | K. Veliyeva, C. G. Aras, S. Bayramov, Some fixed-point type theorems on parametric soft $b$-metric spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 44 (2024), 1–12. |
| [23] |
D. Wardowski, On a soft mapping and its fixed points, Fixed Point Theory Appl., 2013 (2013), 182. https://doi.org/10.1186/1687-1812-2013-182 doi: 10.1186/1687-1812-2013-182
|
| [24] |
M. I. Yazar, C. G. Aras, S. Bayramov, Fixed point theorems of soft contractive mappings, Filomat, 30 (2013), 269–279. https://doi.org/10.2298/FIL1602269Y doi: 10.2298/FIL1602269Y
|
Çiğdem Aras Gündüz, Sadi Bayramov, Arzu Erdem Coşkun. Fixed point theorems of contractive mappings on soft parametric metric space[J]. AIMS Mathematics, 2024, 9(4): 7945-7954. doi: 10.3934/math.2024386
DownLoad: