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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 35 | Number 3 | Year 2016 | Article Id. IJMTT-V35P529 | DOI : https://doi.org/10.14445/22315373/IJMTT-V35P529

Common fixed point theorem in intuitionistic fuzzy metric space using an implicit relation


Aarti Sugandhi, Sandeep Kumar Tiwari, Aklesh Pariya
Abstract

The aim of this paper is to prove some common fixed point theorems for weakly compatible mappings in intuitionistic fuzzy metric spaces satisfying an integral type implicit relation using property (E.A) which generalize results of Aliouche[3],Aliouche and Popa[4],Pathak et al. [11] , Badshah and Pariya [5], Imdad et al. [7], Manro et al.[9] and references mentioned therein from metric spaces , fuzzy metric spaces to intuitionistic fuzzy metric spaces.

Keywords
Intuitionistic fuzzy metric space, weakly compatible mapping, implicit relation.
References

[1] C. Alaca, I. Altun and D.Turkoglu, On compatible mapping of type (I) and (II) in intuitionistic fuzzy metric spaces, Communications of the korean, Mathematical sociaty, (2008)Vol. 23 No. 3,427-446.
[2] C. Alaca, D. Turkoglu and C. Yildiz, , Fixed points in Intuitionistic fuzzy metric space, Smallerit Chaos, soliton & Fractals, 29(5)(2006), 1073-1078.
[3] A. Aliouche,Common fixed point theorems via an implicit relation and new properties, Soochow Journal of Mathematics,(2007) vol. 33 No. 4, 593-601.
[4] A. Aliouche and Popa, Common fixed point theorems for occasionally weakly compatible mappings via implicit relatins,filomat(2008),22.2,99-107.
[5] V.H. Badshah, and A. Pariya, Varahmihir Journal of Mathematical Science, (2009),Vol. 9, 125 – 134.
[6] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Sci. 29 (2002), 531–536.
[7] M. Imdad, Ali,J. and L. Khan, Coincidence and fixed point in symmetric spaces under strict contraction , J. Math. Anal. Appl.(2006),Vol. 320,No.1, 352-360.
[8] G. Jungck and B.E. Rhoades, Fixed point for set valued functions without continuity, I. J. Pure Appl. Math.,29(3)(1998), 227-238.
[9] S. Manro, S.S. Bhatia, and S. Kumar, Common fixed point theorems for weakly compatible maps satisfying common (E.A) property in intuitionistic fuzzy metric spaces using implicit relation, Journal of Advanced Studies in Topology (Egypt)3(2)(2012), 38-44.
[10] J.H. Park, Intuitionistic fuzzy metric space, Chaos, Solitions & Fractals, 22(2004), 1039-1046.
[11] H.K. Pathak, R.Tiwari, and M.S. Khan, A common fixed point theorem satisfying integral type implicit relation. Applied Mathematics E-notes,(2007).7,222-228.
[12] D.Turkoglu, C. Alaca., Y. J. Cho, and C. Yildiz, : Common fixed point theorems in Intuitionistic Fuzzy metric spaces. J. Appl. Math. and Computing, 22(2006), pp. 411 -424.

Citation :

Aarti Sugandhi, Sandeep Kumar Tiwari, Aklesh Pariya, "Common fixed point theorem in intuitionistic fuzzy metric space using an implicit relation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 35, no. 3, pp. 204-210, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V35P529

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