Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
권호 표지
DOI QR코드

DOI QR Code

FIXED POINT RESULTS IN SOFT RECTANGULAR b-METRIC SPACE

  • Sonam (Department of Mathematics, Amity Institute of Applied Sciences, Amity University Kolkata) ;
  • C. S. Chauhan (Department of Applied Mathematics, Institute of Engineering and Technology, Devi Ahilya University) ;
  • Ramakant Bharadwaj (Department of Mathematics, Amity Institute of Applied Sciences, Amity University) ;
  • Satyendra Narayan (Department of Applied Computing, Sheridan Institute of Technology)
  • Received : 2022.12.01
  • Accepted : 2023.01.15
  • Published : 2023.09.15
⟨ Previous Next ⟩

Abstract

The fundamental aim of the proposed work is to introduce the concept of soft rectangular b-metric spaces, which involves generalizing the notions of rectangular metric spaces and b-metric spaces. Furthermore, an investigation into specific characteristics and topological aspects of the underlying generalization of metric spaces is conducted. Moreover, the research establishes fixed point theorems for mappings that satisfy essential criteria within soft rectangular b-metric spaces. These theorems offer a broader perspective on established results in fixed point theory. Additionally, several congruous examples are presented to enhance the understanding of the introduced spatial framework.

Keywords

Acknowledgement

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

References

  1. M. Abbas, G. Murtaza and S. Romaguera, On the fixed point theory of soft metric spaces, Fixed Point Theory Appl., 1 (2016), 1-11.
  2. C.G. Aras, A. Sonmez and H. akall, On soft mappings, arXiv preprint arXiv:1305.4545, 2013.
  3. M. Asim, S. Mujahid and I. Uddin, Fixed point theorems for F-contraction mapping in complete rectangular M-metric space, Appl. General Topo., 23(2) (2022), 363-376. https://doi.org/10.4995/agt.2022.17418
  4. M. Asim, I. Uddin and M. Imdad, Fixed point results in Mv-metric spaces with an application, J. Inequa. Appl., 2019 (2019), 1-19. https://doi.org/10.1186/s13660-019-1955-4
  5. K.V. Babitha and J. Sunil, Soft set relations and functions, Comput. Math. Appl., 60(7) (2010), 1840-1849. https://doi.org/10.1016/j.camwa.2010.07.014
  6. S. Banach, Sur les oprations dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math, 3(1) (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  7. D. Barman, K. Sarkar and K. Tiwary, Some fixed point results on rectangular b-metric space, Facta Universitatis. Series: Math. and Inform., 36(5) (2021), 1033-1045, DOI: https://doi.org/10.22190/FUMI210407075B.
  8. A. Branciari, A fixed point theorem of Banach-Caccippoli type on a class of generalised metric spaces, Publ. Math. Debrecen, 57(1-2) (2000), 31-37. https://doi.org/10.5486/PMD.2000.2133
  9. N. Cagman, S. Karatas and S. Enginoglu, Soft topology, Comput. Math. Appl., 62(1) (2011), 351-358. https://doi.org/10.1016/j.camwa.2011.05.016
  10. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Infor. Unive. Ostraviensis, 1(1) (1993), 511.
  11. S. Das and S.K. Samanta, Soft real sets, soft real numbers and their properties, J. fuzzy Math,, 20(3) (2012), 551-576.
  12. S. Das and S.K. Samanta, Soft metric, Ann. Fuzzy Math. Inform., 6(1) (2013), 77-94.
  13. S. Enginoglu, N. Cagman, S. Karata and T. Aydin, On soft topology, El-Cezer J. Sci. Eng., 2(3) (2015), 23-38. https://doi.org/10.31202/ecjse.67135
  14. R. George, H.A. Nabweg, K.P. Reshma and R. Rajagopalan, Generalized cone b-metric spaces and contraction principles, Mat. Vesn., 67(4) (2015), 246-257.
  15. R. George, S. Radenovic, K.P. Reshma and S. Shukla, Rectangular b-Metric Spaces and Contraction Principle, J. Nonlinear Sci. Appl., 8 (2015), 1005-1013. https://doi.org/10.22436/jnsa.008.06.11
  16. S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl., 62(11) (2011), 4058-4067. https://doi.org/10.1016/j.camwa.2011.09.051
  17. A. Kharal and B. Ahmad, Mappings on fuzzy soft classes, Adv. Fuzzy Syst., 2009, https://doi.org/10.1155/2009/407890.
  18. P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl.,, 45(4-5) (2003), 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
  19. P. Majumdar and S.K. Samanta, On soft mappings, Comput. Math. Appl. 60(9) (2010), 2666-2672. https://doi.org/10.1016/j.camwa.2010.09.004
  20. Z.D. Mitrovic, A note on a Banachs fixed point theorem in b-rectangular metric space and b-metric space, Mathematica Slovaca, 68(5) (2018), 1113-1116. https://doi.org/10.1515/ms-2017-0172
  21. D. Molodtsov, Soft set theoryfirst results, Comput. Math. Appl. 37(4-5) (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
  22. Z. Mostefaoui, M. Bousselsal and J. K. Kim, Some results in fixed point theory concerning rectangular b-metric spaces, Nonlinear Funct. Anal. Appl., 24(1) (2019), 49-59.
  23. D. Pei, and D. Miao, From soft sets to information systems, IEEE International Conference on Granular Computing, 2 (2005), 617-621.
  24. M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl., 61(7) (2011), 1786-1799. https://doi.org/10.1016/j.camwa.2011.02.006
  25. Sonam, R. Bhardwaj and S. Narayan, Fixed point results in soft fuzzy metric spaces, Mathematics, 11(14) (2023), 3189.
  26. D. Wardowski, On a soft mapping and its fixed points, Fixed point theory Appl., 1 (2013), 1-11. https://doi.org/10.1186/1687-1812-2013-182
  27. M.I. Yazar, C. Gunduz and S. Bayramov, Fixed point theorems of soft contractive mappings, Filomat, 30(2) (2016), 269-279. https://doi.org/10.2298/FIL1602269Y
  28. L.A. Zadeh, Fuzzy sets, Inform. control, 8(3) (1965), 338-353.  https://doi.org/10.1016/S0019-9958(65)90241-X