Geodesic
COMPATIBILITY OF TYPE P IN MODIFIED INTUITIONISTIC FUZZY METRIC SPACE
JAIN, SHOBHA1 ; JAIN, SHISHIR2 ; JAIN, LAL BAHADUR3
1 Quantum School of Technology, Roorkee (U.K), India
2 Shri Vaishnav Institute of Technology and Science, Indore (M.P.), India
3 Retd. Principal, Govt. Arts and Commerce College , Indore (M.P.), India
Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 2, p. 96-109.

Voir la notice de l'article provenant de la source International Scientific Research Publications

The object of this paper is to establish unique common fixed point theorems for four self maps satisfying a new contractive condition in a modified intuitionistic fuzzy metric space through compatibility of type (P). A generalization of a result of D Turkoglu et al [J. Apply. Math. Computing (2006)] in the setting of a modified intuitionistic fuzzy metric space follows from them. Modified intuitionistic fuzzy version of Grabiec contraction Principle has also been established. All the results presented in this paper are new. Examples have been constructed in support of the main results of this paper.
DOI : 10.22436/jnsa.003.02.03
Classification : 54H25, 47H10
Keywords: Modified intuitionistic fuzzy metric space, common fixed points, compatible maps of type (P), weak compatible maps, t-norm, t-conorm.

JAIN, SHOBHA 1 ; JAIN, SHISHIR 2 ; JAIN, LAL BAHADUR 3

1 Quantum School of Technology, Roorkee (U.K), India
2 Shri Vaishnav Institute of Technology and Science, Indore (M.P.), India
3 Retd. Principal, Govt. Arts and Commerce College , Indore (M.P.), India 
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JAIN, SHOBHA; JAIN, SHISHIR; JAIN, LAL BAHADUR. COMPATIBILITY OF TYPE P IN MODIFIED INTUITIONISTIC FUZZY METRIC SPACE. Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 2, p. 96-109. doi : 10.22436/jnsa.003.02.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.003.02.03/

[1] Abidi, H.; Cho, Y. J.; Regan, D. O.; Saadati, R. Common fixed point in L-fuzzy metric spaces, Applied Mathematics and Computation , Volume 182 (2006), pp. 820-828

[2] Alaca, C. A common fixed point theorem for weak compatible mappings in intuitionistic fuzzy metric spaces, International Journal of Pure and Applied Math, Volume 32 (2006), pp. 537-548

[3] Alaca, C.; Turkoglu, D.; Yildiz, C. Fixed points in intuitionistic fuzzy metric spaces, Chaos Solitons and Fractals , Volume 29 (2006), pp. 1073-1078

[4] K. Atanassov Intuitionistic fuzzy sets, Fuzzy Sets and System , Volume 20 (1986), pp. 87-96

[5] Atanassov, K. Intuitionistic fuzzy sets, Fuzzy Sets and System , Volume 61 (1994), pp. 137-142

[6] Deschrijver, G.; Cornelis, C.; Kerre, EE. On the representation of intuitionistic fuzzy t-norm and t-conorm, IEEE Trans. Fuzzy Syst, Volume 12 (2004), pp. 45-61

[7] Deschrijver, G.; EE. Kerre On the relationship between some extensions of fuzzy set theory, Fuzzy sets and system , Volume 133 (2003), pp. 227-235

[8] George, A.; Veeramani, P. On some results in fuzzy metric spaces, Fuzzy Sets and System , Volume 64 (1994), pp. 395-399

[9] Grabiec, M. Fixed points in fuzzy metric spaces, Fuzzy Sets and System , Volume 27 (1988), pp. 385-389

[10] Jain, Shobha; Jain, Shishir; Bahadur, Lal r-r'contraction in Modified Intuitionistic fuzzy metric space , Kochi Journal of Mathematics , Volume 4 (2009), pp. 87-100

[11] G. Jungck Commuting maps and fixed points, Amer. Math. monthly , Volume 83 (1976), pp. 261-263

[12] Jungck, G. Compatible mappings and common fixed point, Internat. Journal of Math. Math. Sci., Volume 9 (1986), pp. 771-779

[13] Kramosil, I.; Michalek, J. Fuzzy metric and statistical metric spaces, Kybernetica , Volume 11 (1975), pp. 326-334

[14] Kutukcu, S. A common fixed point theorem for a sequence of self maps in intuitionistic fuzzy metric spaces, Commun. Korean Math. Soc. , Volume 21 (2006), pp. 679-687

[15] Park, J. H. Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals , Volume 22 (2004), pp. 1039-1046

[16] Saadati, R.; Park, J. H. On the intuitionistic fuzzy topolodical spaces, Chaos Solitons and Fractals , Volume 27 (2006), p. 331-44

[17] Saadati, R.; Sedghi, S.; Shobhe, N. Modified Intuitionistic Fuzzy metric spaces and fixed point theorems, Choas Fractal and Solitions ( in press)

[18] Sessa, S. On a weak commutative condition in fixed point consideration Publ. , Inst. Math (Beograd), Volume 32(46) (1982), pp. 146-153

[19] Singh, B.; Jain, Shishir Fixed point theorem for six self-maps in fuzzy metric space, The Journal of Fuzzy Mathematics , Volume 14 (2006), pp. 231-243

[20] Turkoglu, D.; Alaca, C.; Cho, Y. J.; Yildiz, C. Common fixed point theorems in intuitionistic fuzzy metric spaces, J. Apply. Math. Computing, Volume 22 (2006), pp. 411-424

[21] Yousefi, A.; M. Soleimani L-fuzzy nonlinear approximation theory with application, J. Nonlinear Sci. Appl. , Volume 2 (2009), pp. 146-151

[22] Zadeh, L. A. Fuzzy sets, Inform and control , Volume 89 (1965), pp. 338-353

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