A Study on Bipolar Soft \(b\)-Metric Spaces

Authors

  • Pooja Dhawan Department of Mathematics & Humanities, MMEC, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala 133207, Haryana, India https://orcid.org/0000-0002-0665-6444
  • Akshu Grewal Department of Mathematics & Humanities, MMEC, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala 133207, Haryana, India

DOI:

https://doi.org/10.26713/cma.v16i3.3089

Keywords:

b-Metric spaces, Contraction mappings, Bipolar soft metric spaces

Abstract

In this work, bipolar soft \(b\)-metric space is introduced, which is constructed from \(b\)-metric space and several soft point sets. Also, using this framework, several fixed point theorems illustrated using bipolar soft contractive mappings and offer significant clarifications on this idea through medical applications.

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References

M. Abbas, B. Ali and Y. I. Suleiman, Generalized coupled common fixed point results in partially ordered A-metric spaces, Fixed Point Theory and Applications 2015 (2015), article number 64, DOI: 10.1186/s13663-015-0309-2.

M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Computers & Mathematics with Applications 57(9) (2009), 1547 – 1553, DOI: 10.1016/j.camwa.2008.11.009.

I. A. Bakhtin, The contraction mapping principle in quasi-metric spaces, Functional Analysis 30 (1989), 26 – 37.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations integrals, Fundamenta Mathematicae 3 (1922), 133 – 181, DOI: 10.4064/fm-3-1-133-181.

S. Bayramova, C. G. Aras and H. Posul, A study on bipolar soft metric spaces, Filomat 37(10) (2023), 3217 – 3224, DOI: 10.2298/FIL2310217B.

S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1(1) (1993), 5 – 11, URL: http://dml.cz/dmlcz/120469.

S. Das and S. K. Samanta, Soft metric, Annals of Fuzzy Mathematics and Informatics 6(1) (2013), 77 – 94, URL: http://www.afmi.or.kr/papers/2013/Vol-06_No-01/AFMI-6-1(1--226)/AFMI-6-1(77--94)-J-120715R1.pdf.

B. C. Dhage, A Study of Some Fixed Point Theorems, Doctoral Dissertation, Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, India, (1985), URL: http://hdl.handle.net/10603/145768.

P. Dhawan and A. Grewal, Some novel fixed point findings in intuitionistic fuzzy b-metric spaces, in: Intelligent Systems Design and Applications (ISDA 2023), Lecture Notes in Networks and Systems, A. Abraham, A. Bajaj, T. Hanne, P. Siarry and K. Ma (editors), Vol. 1050, Springer, Cham., (2024), DOI: 10.1007/978-3-031-64847-2_2.

P. Dhawan and A. Grewal, b-Multiplicative metric spaces: Coupled coincidence points with application, Journal of Multidisciplinary Mathematics 27(8) (2024), 1909 – 1914, DOI: 10.47974/JIM-2057.

P. Dhawan and Tripti, Fixed point results in soft b-fuzzy metric spaces, Advances in Fixed Point Theory 14 (2024), Article ID 50, DOI: 10.28919/afpt/8773.

M. M. Fréchet, Sur quelques points du calcul fonctionnel, Rend. Circ. Matem. Palermo 22 (1906), 1 – 72, DOI: 10.1007/BF03018603.

C. Gunduz (Aras) and H. Posul, On some new operations in probabilistic soft set theory, European Journal of Pure and Applied Mathematics 9(3) (2016), 333 – 339, URL: https://www.ejpam.com/index.php/ejpam/article/view/2349.

R. Kannan, Some results on fixed points, Bulletin of the Calcutta Mathematical Society 60 (1969), 71 – 76.

P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Computers & Mathematics with Applications 45 (2003), 555 – 562, DOI: 10.1016/S0898-1221(03)00016-6.

S. G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728(1) (1994), 183 – 197, DOI: 10.1111/j.1749-6632.1994.tb44144.x.

D. Molodtsov, Soft set theory—First results, Computers & Mathematics with Applications 37(4-5) (1999), 19 – 31, DOI: 10.1016/S0898-1221(99)00056-5.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis 7 (2006), 289 – 297.

A. Mutlu and U. Gürdal, Bipolar metric spaces and some fixed point theorems, Journal of Nonlinear Sciences and Applications 9(9) (2016), 5362 – 5373, DOI: 10.22436/jnsa.009.09.05.

S. Öztunç, S. Aslan and H. Dutta, Categorical structures of soft groups, Soft Computing 25 (2021), 3059 – 3064, DOI: 10.1007/s00500-020-05362-0.

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Published

30-10-2025
CITATION

How to Cite

Dhawan, P., & Grewal, A. (2025). A Study on Bipolar Soft \(b\)-Metric Spaces. Communications in Mathematics and Applications, 16(3), 1011–1019. https://doi.org/10.26713/cma.v16i3.3089

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Research Article