Soft $S_b$-Metric Spaces and Some of Its Properties | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 12, Issue 1, January 2024, Pages 1-11 PDF (488.48 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2023.233274.1065 | ||
| Authors | ||
| Sk Nazmul1; Utpal Badyakar* 2 | ||
| 1Department of Mathematics, Kazi Nazrul University, Asansol, Paschim Bardwan-713340, India | ||
| 2Department of Mathematics, Bankura Sammilani College, Bankura-722102, India | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| soft set; soft point; soft mapping; soft $S_b$-metric spaces; fixed soft point | ||
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