AM  Vol.4 No.9 A , September 2013
Common New Fixed Point Theorem in Modified Intuitionistic Fuzzy Metric Spaces Using Implicit Relation
ABSTRACT

In this paper, we prove some common fixed point theorems for two pair of compatible and subsequentially continuous mappings satisfying an implicit relation in Modified Intuitionistic fuzzy metric spaces. Consequently, our results improve and sharpen many known common fixed point theorems available in the existing literature of metric fixed point theory.


Cite this paper
S. Manro and S.  , "Common New Fixed Point Theorem in Modified Intuitionistic Fuzzy Metric Spaces Using Implicit Relation," Applied Mathematics, Vol. 4 No. 9, 2013, pp. 27-31. doi: 10.4236/am.2013.49A005.
References
[1]   L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353.
doi:10.1016/S0019-9958(65)90241-X

[2]   A. T. Atanassov, “Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, Vol. 20, No. 1, 1986, pp. 87-96. doi:10.1016/S0165-0114(86)80034-3

[3]   J. H. Park, “Intuitionistic Fuzzy Metric Spaces,” Chaos, Solitons & Fractals, Vol. 22, No. 5, 2004, pp. 1039-1046. doi:10.1016/j.chaos.2004.02.051

[4]   R. Saadati, S. Sedghi and N. Shobhe, “Modified Intuitio nistic Fuzzy Metric Spaces and Some Fixed Point Theo rems,” Chaos, Solitons & Fractals, Vol. 38, No. 1, 2008, pp. 36-47.
doi:10.1016/j.chaos.2006.11.008

[5]   G. Jungck, “Compatible Mappings and Common Fixed Points,” International Journal of Mathematics and Ma thematical Sciences, Vol. 9, No. 4, 1986, pp. 771-779. doi:10.1155/S0161171286000935

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

[7]   S. Sessa, “On a Weak Commutativity Condition in Fixed Point Considerations,” Publications de l’Institut Mathé matique (Beograd), Vol. 34, No. 46, 1982, pp. 149-153.

[8]   H. Bouhadjera and C. Godet-Thobie, “Common Fixed The orems for Pairs of Subcompatible Maps,” 2009.

[9]   D. Gopal and M. Imdad, “Some New Common Fixed Point Theorems in Fuzzy Metric Spaces,” Annali dell’ Univer sità di Ferrara, Vol. 57, No. 2, 2011, pp. 303-316. doi:10.1007/s11565-011-0126-4

[10]   S. Manro, H. Bouharjera and S. Singh, “A Common Fix ed Point Theorem in Intuitionistic Fuzzy Metric Space by Using Sub-Compatible Maps,” International Journal of Contemporary Mathematical Sciences, Vol. 55, No. 55, 2010, pp. 2699-2707.

[11]   G. Deschrijver and E. E. Kerre, “On the Relationship be tween Some Extensions of Fuzzy Set Theory,” Fuzzy Sets and Systems, Vol. 133, No. 2, 2003, pp. 227-235. doi:10.1016/S0165-0114(02)00127-6

[12]   G. Deschrijver, C. Cornelis and E. E. Kerre, “On the Rep resentation of Intuitionistic Fuzzy T-Norm and T-Conorm,” The IEEE Transactions on Fuzzy Systems, Vol. 12, No. 2, 2004, pp. 45-61.
doi:10.1109/TFUZZ.2003.822678

[13]   M. Tanveer, M. Imdad, D. Gopal and D. Kumar, “Com mon Fixed Point Theorem in Modified Intuitionistic Fuz zy Metric Spaces with Common Property (E.A.),” Fixed Point Theory and Applications, Vol. 36, 2012. doi:10.1186/1687-1812-2012-36

[14]   D. Turkoglu, C. Alaca, Y. J. Cho and C. Yildiz, “Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spac es,” Journal of Applied Mathematics and Computing, Vol. 22, No. 1-2, 2006, pp. 411-424. doi:10.1007/BF02896489

[15]   C. Alaca, “A Common Fixed Point Theorem for Weak Compatible Mappings in Intuitionistic Fuzzy Metric Spac es,” International Journal of Pure and Applied Mathe matics, Vol. 32, No. 4, 2006, pp. 25-36.

[16]   S. Manro, S. Kumar and S. S. Bhatia, “Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces Us ing Occasionally Weakly Compatible Maps,” The Journal of Mathematics and Computer Science, Vol. 2, No. 2, 2012, pp. 73-81.

[17]   R. P. Pant, “Common Fixed Foints of Four Mappings,” Bulletin of Calcutta Mathematical Society, Vol. 90, No. 4, 1998, pp. 281-286.

 
 
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