10.57647/

Common Fixed-Point Theorems For Generalized Fuzzy Contraction Mapping

  1. Department of Mathematics, Lorestan University, P. O. Box 465, Khoramabad, Iran.
  2. Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran.

Received: 03-05-2016

Revised: 17-08-2016

Accepted: 24-10-2016

Published in Issue 28-07-2025

How to Cite

Abbasi, N., Mottaghi Golshan, H., & Shakori, M. (2025). Common Fixed-Point Theorems For Generalized Fuzzy Contraction Mapping. International Journal of Mathematical Modelling & Computations, 6(4). https://doi.org/10.57647/

Abstract

In this paper we investigate common fixed point theorems for contraction mapping in fuzzy metric space introduced by Gregori and Sapena [V. Gregori, A. Sapena, On fixedpoint theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252]. 

Keywords

  • Fuzzy metric spaces,
  • Generalized contraction mapping,
  • Common fixed point

References

  1. [1] N. Abbasi and H. Mottaghi Golshan, On best approximation in fuzzy metric spaces, Kybernetica
  2. (Prague), 51 (2) (2015) 374{386.
  3. [2] L. B. Ciri´c, On a family of contractive maps and fixed points, ´ Publ. Inst. Math (Beograd) (N.S),
  4. 17 (31) (1974) 45{51.
  5. [3] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64
  6. (3) (1994) 395{399.
  7. [4] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (3) (1988) 385{389.
  8. [5] V. Gregori and S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Sets and Systems,
  9. Theme: Fuzzy intervals, 130 (3) (2002) 399{404.284 N. Abbasi et al./ IJM2C, 6 - 4 (2016) 277-284.
  10. [6] V. Gregori and S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Sets and
  11. Systems, 144 (3) (2004) 411{420.
  12. [7] V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems,
  13. 125 (2) (2002) 245{252.
  14. [8] D. Mihet¸, Fuzzy -contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and
  15. Systems, 159 (6) (2008) 739{744.
  16. [9] E. Pap, O. Hadˇzi´c and R. Mesiar, A fixed point theorem in probabilistic metric spaces and an
  17. application, J. Math. Anal. Appl, 202 (2) (1996) 433{449.
  18. [10] J. Rodr´ıguez-L´opez and S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets
  19. and Systems, 147 (2) (2004) 273{283.
  20. [11] S. Romaguera, A. Sapena and P. Tirado. The Banach fixed point theorem in fuzzy quasi-metric
  21. spaces with application to the domain of words, Topology Appl, 154 (10) (2007) 2196{2203.
  22. [12] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math, 10 (1960) 313{334.
  23. [13] R. M. Tardiff, Contraction maps on probabilistic metric spaces, J. Math. Anal. Appl, 165 (2)
  24. (1992) 517{523.