COMMON FIXED POINTS OF COMPATIBLE MAPS OF TYPE (β) ON FUZZY METRIC SPACES

Title & Authors
COMMON FIXED POINTS OF COMPATIBLE MAPS OF TYPE (β) ON FUZZY METRIC SPACES
KUTUKCU SERVET; TURKOGLU DURAN; YILDIZ CEMIL;

Abstract
In this paper we prove a common fixed point theorem for compatible maps of type $\small{(\beta)}$ on fuzzy metric spaces with arbitrary continuous t-norm.
Keywords
fuzzy metric spaces;common fixed point;
Language
English
Cited by
1.
A COMMON FIXED POINT THEOREM FOR A SEQUENCE OF SELF MAPS IN INTUITIONISTIC FUZZY METRIC SPACES,;

대한수학회논문집, 2006. vol.21. 4, pp.679-687
2.
COMMON FIXED POINT OF COMPATIBLE MAPS OF TYPE (γ) ON COMPLETE FUZZY METRIC SPACES,;;;

대한수학회논문집, 2009. vol.24. 4, pp.581-594
3.
On Fixed Point Theorem of Weak Compatible Maps of Type(γ) in Complete Intuitionistic Fuzzy Metric Space,;

International Journal of Fuzzy Logic and Intelligent Systems, 2011. vol.11. 1, pp.38-43
1.
Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property, Applied Mathematics, 2012, 03, 09, 976
2.
On Fixed Point Theorem of Weak Compatible Maps of Type(γ) in Complete Intuitionistic Fuzzy Metric Space, International Journal of Fuzzy Logic and Intelligent Systems, 2011, 11, 1, 38
References
1.
S. Banach, Theorie les operations lineaires, Manograie Mathematyezne, Warsaw, Poland, 1932

2.
Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy Math. 4 (1997), 949-962

3.
Y. J. Cho, H. K. Pathak, S. M. Kang, and J. S. Jung, Common fixed points of compatible maps of type (${\beta}$) on fuzzy metric spaces, Fuzzy Sets and Systems 93 (1998), 99-111

4.
Z. K. Deng, Fuzzy pseduo-metric spaces, J. Math. Anal. Appl. 86 (1982), 74-95

5.
M. Edelstein, On fixed and periodic points under contraction mappings, J. London Math. Soc. 37 (1962) 74-79

6.
M. A. Erceg, Metric spaces in fuzzy set theory, J. Math. Anal. Appl. 69 (1979), 205-230

7.
J. X. Fang, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 46 (1992), 107-113

8.
A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399

9.
M. Grabiec, Fixed points in fuzzy metric space, Fuzzy Sets and Systems 27 (1988), 385-389

10.
O. Hadzic and E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Acad. Publ., 2001

11.
O. Hadzic and E. Pap, A fixed point theorem for multivalued mappins in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Sets and Systems 127 (2002), 333-344

12.
I. Istratescu, A fixed point theorem for mappings with a probabilistic contractive iterate, Rev. Roumaire. Math. Pure Appl. 26 (1981), 431-435

13.
G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261-263

14.
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), 771-779

15.
O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984), 215-229

16.
E. P. Klement, R. Mesiar, and E. Pap, Triangular norms. Position paper I: Basic analytical and algebraic properties, Fuzzy Sets and Systems 143 (2004), 5-16

17.
E. P. Klement, R. Mesiar, and E. Pap, Problems on triangular norms and related operators, Fuzzy Sets and Systems 145 (2004), 471-479

18.
O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika (Praha) 11 (1975), 326-334

19.
S. N. Mishra, N. Sharma, and S. L. Singh, Common fixed points of maps on fuzzy metric spaces, Internat. J. Math. Sci. 17 (1994), 253-258

20.
H. K. Pathak, Y. J. Cho, S. S. Chang, and S. M. Kang, Compatible mappings of type (P), Rev. Res. Univ. Novi Sad., to appear

21.
B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290

22.
B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334

23.
V. M. Sehgal and A. T. Bharucha-Reid, Fixed point of contraction mapping on PM spaces, Math. Systems Theory 6 (1972), 97-100

24.
S. Sessa, On weak commutativity condition of mappings in fixed point consider- ations, Publ. Inst. Math. Beagrad 32 (46) (1982), 149-153

25.
S. Sharma, Common Fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 127 (2002), 345-352

26.
S. L. Singh and S. Kasahara, On some recent results on common fixed points, Indian J. Pure Appl. Math. 13 (1982), 757-761

27.
S. L. Singh and B. Ram, Common fixed points of commuting mappings in 2- metric spaces, Math. Sem. Notes Kobe Univ. 10 (1982), 197-208

28.
L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353