ON COMPATIBLE MAPPINGS OF TYPE (I) AND (II) IN INTUITIONISTIC FUZZY METRIC SPACES

Title & Authors
ON COMPATIBLE MAPPINGS OF TYPE (I) AND (II) IN INTUITIONISTIC FUZZY METRIC SPACES
Alaca, Cihangir; Altun, Ishak; Turkoglu, Duran;

Abstract
In this paper, we give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and we prove a common fixed point theorem for four mappings under the condition of compatible mappings of type (I) and of type (II) in complete intuitionistic fuzzy metric spaces.
Keywords
intuitionistic fuzzy metric space;common fixed point;compatible mappings and compatible mappings of types $\small{({\alpha})}$$\small{({\beta})}$;(I) and (II);
Language
English
Cited by
1.
Fixed Point Theorem for Compatible Maps with Type(I) and (II) in Intuitionistic Fuzzy Metric Space,;

International Journal of Fuzzy Logic and Intelligent Systems, 2010. vol.10. 3, pp.194-199
1.
Some new fixed point results on intuitionistic fuzzy metric spaces, Cogent Mathematics, 2016, 3, 1
2.
Fixed Point Theorem for Compatible Maps with Type(I) and (II) in Intuitionistic Fuzzy Metric Space, International Journal of Fuzzy Logic and Intelligent Systems, 2010, 10, 3, 194
3.
Common fixed point theorems for families of maps in complete L-fuzzy metric spaces, Filomat, 2009, 23, 3, 67
4.
Common fixed point theorems for families of compatible mappings in intuitionistic fuzzy metric spaces, ANNALI DELL'UNIVERSITA' DI FERRARA, 2010, 56, 2, 305
5.
Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces, Applied Mathematics, 2010, 01, 06, 510
References
1.
C. Alaca, D. Turkoglu, and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals 29 (2006), 1073-1078

2.
S. Banach, Theorie les operations lineaires, Manograie Mathematyezne Warsaw Poland, 1932

3.
Z. K. Deng, Fuzzy pseudo-metric spaces, J. Math. Anal. Appl. 86 (1982), 74-95

4.
M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74-79

5.
M. A. Erceg, Metric spaces in fuzzy set theory, J. Math. Anal. Appl. 69 (1979), 338-353

6.
J. X. Fang, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 46 (1992), 107-113

7.
A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399

8.
M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1988), 385-389

9.
V. Gregori, S. Romaguera, and P. Veeramani, A note on intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals 28 (2006), 902-905

10.
G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly. 83 (1976), 261-263

11.
O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984), 215-229

12.
I. Kramosil and J. Michalek, Fuzzy metric and Statistical metric spaces, Kybernetica 11 (1975), 326-334

13.
R. Lowen, Fuzzy Set Theory, Kluwer Academic Pub., Dordrecht 1996

14.
D. Mihet¸, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems 158 (2007), 915-921

15.
R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), 436-440

16.
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals 22 (2004), 1039-1046

17.
J. S. Park, Y. C. Kwun, and J. H. Park, A fixed point theorem in the intuitionistic fuzzy metric spaces, Far East J. Math. Sci. 16 (2005), 137-149

18.
R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons & Fractals 27 (2006), 331-344

19.
B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 314-334

20.
D. Turkoglu, C. Alaca, Y. J. Cho, and C. Yildiz, Common fixed point theorems in intuitionistic fuzzy metric spaces, J. Appl. Math. & Computing 22 (2006), 411-424

21.
D. Turkoglu, C. Alaca, and C. Yildiz, Compatible maps and compatible maps of types (${\alpha}$) and (${\beta}$) in intuitionistic fuzzy metric spaces, Demonstratio Math. 39 (2006), 671-684

22.
D. Turkoglu, I. Altun, and Y. J. Cho, Common fixed points of compatible mappings of type (I) and (II) in fuzzy metric spaces, J. Fuzzy Math. 15 (2007), 435-448

23.
L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353