Topological Properties and Fixed Point Results for Modified Intuitionistic Generalized Fuzzy Metric Spaces

Main Article Content

Vishal Gupta, Ashima Kanwar, Rahul Shukla

Abstract

The principle originality inside the paper is to establish the concept of modified intuitionistic generalized fuzzy metric space and its fundamental topological properties. Moreover, we give the steps for proving some coupled coincidence point results for mapping with contractive condition in partial ordered modified intuitionistic generalized fuzzy metric space. Furthermore, an illustration is proved in the support of our main result.

Article Details

References

  1. M. Abbas, B. Ali, Y.I. Suleiman, Generalized Coupled Common Fixed Point Results in Partially Ordered A-Metric Spaces, Fixed Point Theory Appl. 2015 (2015), 64. https://doi.org/10.1186/s13663-015-0309-2.
  2. C. Alaca, D. Turkoglu, C. Yildiz, Fixed Points in Intuitionistic Fuzzy Metric Spaces, Chaos Solitons Fractals 29 (2006), 1073–1078. https://doi.org/10.1016/j.chaos.2005.08.066.
  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. R. Bhardwaj, A. Sharma, N. Mani, K. Kumar, An Intuitionistic Fuzzy Entropy Measure and Its Application in MultiAttribute Decision Making With Incomplete Weights Information:, in: S. Broumi (Ed.), Advances in Computer and Electrical Engineering, IGI Global, 2022: pp. 324–338. https://doi.org/10.4018/978-1-7998-7979-4.ch015.
  5. T.G. Bhaskar, V. Lakshmikantham, Fixed Point Theorems in Partially Ordered Metric Spaces and Applications, Nonlinear Anal.: Theory Methods Appl. 65 (2006), 1379–1393. https://doi.org/10.1016/j.na.2005.10.017.
  6. M. Bukatin, R. Kopperman, S. Matthews, H. Pajoohesh, Partial Metric Spaces, Amer. Math. Mon. 116 (2009), 708–718. https://doi.org/10.4169/193009709X460831.
  7. D. Çoker, An Introduction to Intuitionistic Fuzzy Topological Spaces, Fuzzy Sets Syst. 88 (1997), 81–89. https://doi.org/10.1016/S0165-0114(96)00076-0.
  8. G. Deschrijver, C. Cornelis, E.E. Kerre, On the Representation of Intuitionistic Fuzzy t-Norms and t-Conorms, IEEE Trans. Fuzzy Syst. 12 (2004), 45–61. https://doi.org/10.1109/TFUZZ.2003.822678.
  9. G. Deschrijver, E.E. Kerre, On the Relationship between Some Extensions of Fuzzy Set Theory, Fuzzy Sets Syst. 133 (2003), 227–235. https://doi.org/10.1016/S0165-0114(02)00127-6.
  10. 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.
  11. V. Gregori, S. Romaguera, P. Veeramani, A Note on Intuitionistic Fuzzy Metric Spaces, Chaos Solitons Fractals 28 (2006), 902–905. https://doi.org/10.1016/j.chaos.2005.08.113.
  12. V. Gupta, A. Gondhi, R. Shukla, Fixed Point Results in Modified Intuitionistic Fuzzy Soft Metric Spaces with Application, Mathematics 12 (2024), 1154. https://doi.org/10.3390/math12081154.
  13. X.Q. Hu, Q. Luo, Coupled Coincidence Point Theorems for Contractions in Generalized Fuzzy Metric Spaces, Fixed Point Theory Appl. 2012 (2012), 196. https://doi.org/10.1186/1687-1812-2012-196.
  14. I. Kramosil, J. Michalek, Fuzzy Metric and Statistical Metric Spaces, Kybernetica 11 (1975), 336-344.
  15. G. Mani, A.J. Gnanaprakasam, S. Kumar, O. Ege, M. De La Sen, Fixed-Point Theorems for Nonlinear Contraction in Fuzzy-Controlled Bipolar Metric Spaces, Axioms 12 (2023), 396. https://doi.org/10.3390/axioms12040396.
  16. N. Mani, M. Pingale, R. Shukla, R. Pathak, Fixed Point Theorems in Fuzzy b-Metric Spaces Using Two Different t-Norms, Adv. Fixed Point Theory 13 (2023), 29. https://doi.org/10.28919/afpt/8235.
  17. Z. Mustafa, B. Sim, A New Approach to Generalized Metric Spaces, J. Nonlinear Convex Anal. 7 (2006), 289-297.
  18. R. Saadati, J.H. Park, On the Intuitionistic Fuzzy Topological Spaces, Chaos Solitons Fractals 27 (2006), 331–344. https://doi.org/10.1016/j.chaos.2005.03.019.
  19. R. Saadati, A. Razani, H. Adibi, A Common Fixed Point Theorem in L-Fuzzy Metric Spaces, Chaos Solitons Fractals 33 (2007), 358–363. https://doi.org/10.1016/j.chaos.2006.01.023.
  20. R. Saadati, S. Sedghi, N. Shobe, Modified Intuitionistic Fuzzy Metric Spaces and Some Fixed Point Theorems, Chaos Solitons Fractals 38 (2008), 36–47. https://doi.org/10.1016/j.chaos.2006.11.008.
  21. S. Sedghi, N. Shobe, H. Zhou, A Common Fixed Point Theorem in D*-Metric Spaces, Fixed Point Theory Appl. 2007 (2007), 027906. https://doi.org/10.1155/2007/27906.
  22. S. Sedghi, N. Shobe, A. Aliouche, A Generalization of Fixed Point Theorems in S-Metric Spaces, Mat. Vesnik 64 (2012), 258-266.
  23. R. Shukla, W. Sinkala, Convex (α, β)-Generalized Contraction and Its Applications in Matrix Equations, Axioms 12 (2023), 859. https://doi.org/10.3390/axioms12090859.
  24. S. Shukla, S. Rai, R. Shukla, Some Fixed Point Theorems for α-Admissible Mappings in Complex-Valued Fuzzy Metric Spaces, Symmetry 15 (2023), 1797. https://doi.org/10.3390/sym15091797.
  25. S. Shukla, N. Dubey, R. Shukla, I. Mezník, Coincidence Point of Edelstein Type Mappings in Fuzzy Metric Spaces and Application to the Stability of Dynamic Markets, Axioms 12 (2023), 854. https://doi.org/10.3390/axioms12090854.
  26. F. Basar, R. Çolak, eds., Summability Theory And Its Applications, Bentham Science Publishers, 2012. https://doi.org/10.2174/97816080545231120101.
  27. M. Mursaleen, F. Ba¸sar, Sequence Spaces: Topics in Modern Summability Theory, CRC Press, 2020. https://doi.org/10.1201/9781003015116.
  28. G. Sun, K. Yang, Generalized Fuzzy Metric Spaces with Properties, Res. J. Appl. Sci. Eng. Technol. 2 (2010), 673-678.
  29. L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.