Back
 AM  Vol.1 No.6 , December 2010
Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces
Abstract: In this paper, we introduce the concept of – chainable intuitionistic fuzzy metric space akin to the notion of – chainable fuzzy metric space introduced by Cho, and Jung [1] and prove a common fixed point theorem for weakly compatible mappings in this newly defined space.
Cite this paper: nullS. Manro, S. Kumar and S. Singh, "Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces," Applied Mathematics, Vol. 1 No. 6, 2010, pp. 510-514. doi: 10.4236/am.2010.16067.
References

[1]   S. H. Cho and J. H. Jung, “On Common Fixed Point Theorems in Fuzzy Metric Spaces,” International Mathematical Forum, Vol. 1, No. 29, 2006, pp. 1441-1451.

[2]   K. Atanassov, “Intuitionistic Fuzzy Sets,” Fuzzy Sets and System, Vol. 20, No. 1, 1986, pp. 87-96.

[3]   D. Coker, “An Introduction to Intuitionistic Fuzzy Topological Spaces,” Fuzzy Sets and System, Vol. 88, No. 1, 1997, pp. 81-89.

[4]   C. Alaca, D. Turkoglu and C. Yildiz, “Fixed Points in Intuitionistic Fuzzy Metric Spaces,” Chaos, Solitons & Fractals, Vol. 29, No. 5, 2006, pp. 1073-1078.

[5]   S. Banach, “Theorie Les Operations Lineaires, Manograie Mathematyezne Warsaw Poland,” In French, Z Subwencji Funduszu Kultury Narodowej, New York, 1932.

[6]   D. Turkoglu, C. Alaca, Y. J. Cho and C. Yildiz, “Common Fixed Point Theorems in Intuitionistic Fuzzy Metric spaces,” Journal of Applied Mathematics and Computing, Vol. 22, No. 1-2, 2006, pp. 411-424.

[7]   G. Jungck, “Commuting Mappings and Fixed Points,” American Mathematical Monthly, Vol. 83, No. 4, 1976, pp. 261-263.

[8]   R. P. Pant, “Common Fixed Points of Noncommuting Mappings,” Journal of Mathematical Analysis and Applications, Vol. 188, No. 2, 1994, pp. 436-440.

[9]   V. Gregori, S. Romaguera and P. Veeramani, “A Note on Intuitionistic Fuzzy Metric Spaces,” Chaos, Solitons & Fractals, Vol. 28, No. 4, 2006, pp. 902-905.

[10]   R. Saadati and J. H. Park, “On the Intuitionistic Fuzzy Topological Spaces,” Chaos, Solitons & Fractals, Vol. 27, No. 2, 2006, pp. 331-344.

[11]   M. Grabiec, “Fixed Points in Fuzzy Metric Spaces,” Fuzzy Sets and Systems, Vol. 27, No. 3, 1988, pp. 385-389.

[12]   M. Imdad and Javid Ali, “Some Common Fixed Point Theorems in Fuzzy Metric Spaces,” Mathematical Communication, Vol. 11, No. 12, 2006, pp. 153-163.

[13]   J. H. Park, “Intuitionistic Fuzzy Metric Spaces,” Chaos, Solitons & Fractals, Vol. 22, No. 52004, pp. 1039-1046.

[14]   J. S. Park, Y. C. Kwun and J. H. Park, “A Fixed Point Theorem in the Intuitionistic Fuzzy Metric Spaces,” Far East Journal of Mathematical Sciences, Vol. 16, No. 2, 2005, pp. 137-149.

[15]   D. Turkoglu, C. Alaca and C. Yildiz, “Compatible Maps and Compatible Maps of Types (α) and (β) in Intuitionistic Fuzzy Metric Spaces,” Demonstration Mathematica, Vol. 39, No. 3, 2006, pp. 671-684.

[16]   B. Schweizer and A. Sklar, “Statistical Metric Spaces,” Paci?c Journal Mathematic, Vol. 10, 1960, pp. 314-334.

[17]   C. Alaca, I. Altun and D. Turkoglu, “On Compatible Mappings of Type (I) and Type (II) in Intuitionistic Fuzzy Metric Spaces,” Korean Mathematical Society, Vol. 23, No. 3, 2008, pp. 427-446.

[18]   G. Jungck, “Compatible Mappings and Common Fixed Points,” International Journal of Mathematics and Mathematical Sciences, Vol. 9, No. 4, 1986, pp. 771-779.

[19]   G. Jungck and B. E. Rhoades, “Fixed Point for Set Valued Functions without Continuity,” Indian Journal of Pure and Applied Mathematics, Vol. 29, No. 3, 1998, pp. 227-238.

 
 
Top