In this study, we have first introduced a generalized concept of soft S-metric space based on soft points of soft sets and renamed it "Soft $S_b$-Metric Space". We have also discussed the relation between soft S-metric spaces and soft $S_b$-metric spaces with an example. After that, we gave some definitions with examples (such as symmetric soft $S_b$-metric spaces, convergent of a sequence of soft points, Cauchy sequence, completeness etc.). Next, we have proved some properties regarding soft $S_b$-metric spaces with example. Then, we have proved some important results on soft $S_b$-metric spaces. Finally, we have proved a unique common fixed point theorem of two soft mappings satisfying a few conditions and with the help of this result we have proved a corollary that if these two soft mappings are the same then we can get a unique fixed soft point. We have also discussed this corollary in details with a suitable example as its application.
Nazmul, S., & Badyakar, U. (2024). Soft $S_b$-Metric Spaces and Some of Its Properties. Electronic Journal of Mathematical Analysis and Applications, 12(1), 1-11. doi: 10.21608/ejmaa.2023.233274.1065
MLA
Sk Nazmul; Utpal Badyakar. "Soft $S_b$-Metric Spaces and Some of Its Properties". Electronic Journal of Mathematical Analysis and Applications, 12, 1, 2024, 1-11. doi: 10.21608/ejmaa.2023.233274.1065
HARVARD
Nazmul, S., Badyakar, U. (2024). 'Soft $S_b$-Metric Spaces and Some of Its Properties', Electronic Journal of Mathematical Analysis and Applications, 12(1), pp. 1-11. doi: 10.21608/ejmaa.2023.233274.1065
VANCOUVER
Nazmul, S., Badyakar, U. Soft $S_b$-Metric Spaces and Some of Its Properties. Electronic Journal of Mathematical Analysis and Applications, 2024; 12(1): 1-11. doi: 10.21608/ejmaa.2023.233274.1065
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