Fixed Point Theorems for zContractions in Intuitionistic Fuzzy Metric Space using Fuzzy Simulation Function

International Journal of Mathematics Trends and Technology (IJMTT)  
© 2022 by IJMTT Journal  
Volume68 Issue8  
Year of Publication : 2022  
Authors : Deepika, Manoj Kumar 

10.14445/22315373/IJMTTV68I8P512 
How to Cite?
Deepika, Manoj Kumar, "Fixed Point Theorems for zContractions in Intuitionistic Fuzzy Metric Space using Fuzzy Simulation Function," International Journal of Mathematics Trends and Technology, vol. 68, no. 8, pp. 129135, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTTV68I8P512
Abstract
In this paper, we establish fixed point theorem for five tuples using the concept of simulation function, zcontraction and fuzzy simulation function in intuitionistic fuzzy metric space.
Keywords : Intuitionistic fuzzy metric space, zcontraction, Simulation function, Fuzzy simulation function.
Reference
[1] C. Alaca, D. Turkoglu, and C.Yildiz, “Fixed Points in Intuionistic Fuzzy Metric Spaces”, Chaos Solitons and Fractals, vol. 29, pp. 10731078, 2006.
[2] K. Atanassov, “Intuitionistic Fuzzy sets, Fuzzy Sets and System”, vol. 20, pp. 8796, 1986.
[3] B. Schweizer, and A. Sklar, “Statistical Metric Spaces”, Pacific. J. Math., vol. 10, pp. 313334, 1960.
[4] L. A. Zadeh, “Fuzzy sets”, Inform. Control, vol. 8, pp. 338345, 1965.
[5] C. Alaca, I. Altun, and D. Turkoglu, “On Compatible Mappings of Type (I) and (II) in Intuionistic Fuzzy Metric Spaces”, Communications of the Korean Mathematical Society, vol. 23, pp. 427446, 2008.
[6] A. Branciari, “A Fixed Point Theorem for Mappings Satisfying a General Contractive Condition of Integral Type”, International Journal of Mathematics and Mathematical Sciences, vol. 29, pp. 531536, 2002.
[7] B. Singh, S. Jain, “Weak Compatibility and Fixed Point Theorems in Fuzzy Metric Spaces”, Ganita, vol. 56, no. 2, pp. 167176, 2005.
[8] W. Sintunavarat, P. Kuman, “Common Fixed Point Theorems for a Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces”, Journal of Applied Mathematics, 2011, Article ID 637958, 14 pages, 2011.
[9] A. George, and P. Veeramani, “On Some Results in Fuzzy Metric Spaces”, Fuzzy Sets and Systems, vol. 64, pp. 395399, 1994.
[10] M. Grabiec, “Fixed Point in Fuzzy Metric Spaces, Fuzzy Sets and Systems”, vol. 27, pp. 385389, 1988.
[11] S. N. Mishra, N. Sharma, and S. L. Singh, “Common Fixed Points of Maps in Fuzzy Metric Spaces”, Internat. J. Math. Math. Sci., vol. 17, pp. 253258.
[12] B. Schweizer, and A. Sklar, “Statistical Metric Spaces”, Pacific. J. Math., vol. 10, pp. 313334, 1960.
[13] B. Singh, S. Jain, “Weak Compatibility and Fixed Point Theorems in Fuzzy Metric Spaces”, Ganita, vol. 56, no. 2, pp. 167176, 2005.
[14] W. Sintunavarat, P. Kuman, “Common Fixed Point Theorems for a Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces”, Journal of Applied Mathematics, 2011, Article ID 637958, 14 pages, 2011.
[15] L. A. Zadeh, “Fuzzy Sets”, Inform. Control, vol. 8, pp. 338345, 1965.
[16] M. S. Khan, “Fixed Point Theorem by Altering Distance Between the Points”, Bulletin of the Australian Mathematical Society, vol. 30, pp. 19, 1984.