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.

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.

nullS. Manro, S. Kumar and S. Singh, "Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces,"

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.

[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.