New Fixed Point Results in Neutrosophic b-Metric Spaces With Application

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-73
Published: Jul 27, 2023
Cite as:
Muhammad Saeed, Umar Ishtiaq, Doha A. Kattan, Khaleel Ahmad, Salvatore Sessa, New Fixed Point Results in Neutrosophic b-Metric Spaces With Application, Int. J. Anal. Appl., 21 (2023), 73.

Main Article Content

Muhammad Saeed, Umar Ishtiaq, Doha A. Kattan, Khaleel Ahmad, Salvatore Sessa

Abstract

In this manuscript, we establish the notion of neutrosophic b-metric spaces as a generalization of fuzzy b-metric spaces, intuitionistic fuzzy b-metric spaces and neutrosophic metric spaces in which three symmetric properties plays an important role for membership, non-membership and neutral functions as well we derive some common fixed point and coincident point results for contraction mappings. Also, we provide several non-trivial examples with graphical views of neutrosophic b-metric spaces and contraction mappings by using computational techniques. Our results are more generalized with respect to the existing ones in the literature. At the end of the paper, we provide an application to test the validity of the main result.

Article Details

References

  1. S. Banach, Sur les Oprations dans les Ensembles Abstraits et Leur Application aux Quations Intgrales, Fund. Math. 3 (1922), 133-181.
  2. L. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X.
  3. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87-96. https://doi.org/10.1016/s0165-0114(86)80034-3.
  4. S. Bhunia, G. Ghorai, M.A. Kutbi, M. Gulzar, M.A. Alam, On the Algebraic Characteristics of Fuzzy Sub e-Groups, J. Funct. Spaces. 2021 (2021), 5253346. https://doi.org/10.1155/2021/5253346.
  5. M. Gulzar, D. Alghazzawi, M.H. Mateen, N. Kausar, A Certain Class of t-Intuitionistic Fuzzy Subgroups, IEEE Access. 8 (2020), 163260–163268. https://doi.org/10.1109/access.2020.3020366.
  6. M. Gulzar, M.H. Mateen, D. Alghazzawi, N. Kausar, A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory, IEEE Access. 8 (2020), 196075–196085. https://doi.org/10.1109/access.2020.3034626.
  7. S. Kanwal, A. Azam, Common Fixed Points of Intuitionistic Fuzzy Maps for Meir-Keeler Type Contractions, Adv. Fuzzy Syst. 2018 (2018), 1989423. https://doi.org/10.1155/2018/1989423.
  8. Z. Deng, Fuzzy Pseudo-Metric Spaces, J. Math. Anal. Appl. 86 (1982), 74–95. https://doi.org/10.1016/0022-247x(82)90255-4.
  9. M.A. Erceg, Metric Spaces in Fuzzy Set Theory, J. Math. Anal. Appl. 69 (1979), 205–230. https://doi.org/10.1016/0022-247x(79)90189-6.
  10. O. Kaleva, S. Seikkala, On Fuzzy Metric Spaces, Fuzzy Sets Syst. 12 (1984), 215–229. https://doi.org/10.1016/0165-0114(84)90069-1.
  11. I. Kramosil, J. Michalek, Fuzzy Metric and Statistical Metric Spaces, Kybernetica, 11 (1975), 326–334. http://dml.cz/dmlcz/125556.
  12. A. George, P. Veeramani, On Some Results in Fuzzy Metric Spaces, Fuzzy Sets Syst. 64 (1994), 395–399. https://doi.org/10.1016/0165-0114(94)90162-7.
  13. S.U. Rehman, H. Aydi, Rational Fuzzy Cone Contractions on Fuzzy Cone Metric Spaces with an Application to Fredholm Integral Equations, J. Funct. Spaces. 2021 (2021), 5527864. https://doi.org/10.1155/2021/5527864.
  14. I.A. Bakhtin, The Contraction Mapping Principle in Quasi Metric Spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26–37.
  15. N. Saleem, U. Ishtiaq, L. Guran, M.F. Bota, On Graphical Fuzzy Metric Spaces With Application to Fractional Differential Equations, Fractal Fract. 6 (2022), 238. https://doi.org/10.3390/fractalfract6050238.
  16. S. Nadaban, Fuzzy b-Metric Spaces, Int. J. Computers, Commun. Control, 11 (2016), 273–281.
  17. U. Ishtiaq, A. Hussain, H. Al Sulami, Certain New Aspects in Fuzzy Fixed Point Theory, AIMS Math. 7 (2022), 8558–8573. https://doi.org/10.3934/math.2022477.
  18. S. Kanwal, D. Kattan, S. Perveen, S. Islam, M.S. Shagari, Existence of Fixed Points in Fuzzy Strong b-Metric Spaces, Math. Probl. Eng. 2022 (2022), 2582192. https://doi.org/10.1155/2022/2582192.
  19. J.H. Park, Intuitionistic Fuzzy Metric Spaces, Chaos Solitons Fractals. 22 (2004), 1039–1046. https://doi.org/10.1016/j.chaos.2004.02.051.
  20. G. Jungck, Commuting Mappings and Fixed Points, Amer. Math. Mon. 83 (1976), 261–263. https://doi.org/10.1080/00029890.1976.11994093.
  21. G. Jungck, Compatible Mappings and Common Fixed Points, Int. J. Math. Math. Sci. 9 (1986), 771–779. https://doi.org/10.1155/s0161171286000935.
  22. D. Turkoglu, C. Alaca, Y.J. Cho, C. Yildiz, Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces, J. Appl. Math. Comput. 22 (2006), 411–424. https://doi.org/10.1007/bf02896489.
  23. G. Jungck, B. E. Rhoades, Fixed-Point Theorems for Occasionally Weakly Compatible Mappings, Fixed Point Theory, 7 (2006), 286–296.
  24. M. Grabiec, Fixed Points in Fuzzy Metric Spaces, Fuzzy Sets Syst. 27 (1988), 385–389. https://doi.org/10.1016/0165-0114(88)90064-4.
  25. B. Schweizer, A. Sklar, Statistical Metric Spaces, Pac. J. Math. 10 (1960), 14–34.
  26. S. Kanwal, A. Azam, F.A. Shami, On Coincidence Theorem in Intuitionistic Fuzzy b-Metric Spaces with Application, J. Funct. Spaces. 2022 (2022), 5616824. https://doi.org/10.1155/2022/5616824.
  27. F. Smarandache, Neutrosophic Set, A Generalisation of the Intuitionistic Fuzzy Sets, Int. J. Pure Appl. Math. 24 (2005), 287–297.
  28. M. Kirişci, N. Şimşek, Neutrosophic Metric Spaces, Math Sci. 14 (2020), 241–248. https://doi.org/10.1007/s40096-020-00335-8.
  29. N. Şimşek, and M. Kirişci, Fixed Point Theorems in Neutrosophic Metric Spaces, Sigma J. Eng. Nat. Sci. 10 (2019), 221-230.
  30. U. Ishtiaq, K. Javed, F. Uddin, M. de la Sen, K. Ahmed, M.U. Ali, Fixed Point Results in Orthogonal Neutrosophic Metric Spaces, Complexity. 2021 (2021), 2809657. https://doi.org/10.1155/2021/2809657.
  31. P. Debnath, A Mathematical Model Using Fixed Point Theorem for Two-Choice Behavior of Rhesus Monkeys in a Noncontingent Environment, in: P. Debnath, N. Konwar, S. Radenović (Eds.), Metric Fixed Point Theory, Springer Nature Singapore, Singapore, 2021: pp. 345–353. https://doi.org/10.1007/978-981-16-4896-0_15.
  32. V. Todorčević, Subharmonic Behavior and Quasiconformal Mappings, Anal. Math. Phys. 9 (2019), 1211–1225. https://doi.org/10.1007/s13324-019-00308-8.
  33. S. Aleksić, Z.D. Mitrović, S. Radenović, Picard Sequences in b-Metric Spaces, Fixed Point Theory. 21 (2020), 35–46. https://doi.org/10.24193/fpt-ro.2020.1.03.