Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces
-
1610
Downloads
-
3045
Views
Authors
Sunny Chauhan
- Near Nehru Training Centre, H. No. 274, Nai Basti B-14, Bijnor-246701, Uttar Pradesh, India.
Wasfi Shatanawi
- Department of Mathematics, Hashemite University, Zarqa, Jordan.
Suneel Kumar
- Government Higher Secondary School, Sanyasiowala PO-Japsur, 244712, Uttarakhand, India.
Stojan Radenović
- Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.
Abstract
In this paper, utilizing the concept of common limit range property, we prove integral type common fixed
point theorems for two pairs of weakly compatible mappings satisfying \(\phi\)-contractive conditions in modified
intuitionistic fuzzy metric spaces. We give some examples to support the useability of our results. We
extend our results to four finite families of self mappings by using the notion of pairwise commuting.
Share and Cite
ISRP Style
Sunny Chauhan, Wasfi Shatanawi, Suneel Kumar, Stojan Radenović, Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 1, 28--41
AMA Style
Chauhan Sunny, Shatanawi Wasfi, Kumar Suneel, Radenović Stojan, Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces. J. Nonlinear Sci. Appl. (2014); 7(1):28--41
Chicago/Turabian Style
Chauhan, Sunny, Shatanawi, Wasfi, Kumar, Suneel, Radenović, Stojan. "Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces." Journal of Nonlinear Sciences and Applications, 7, no. 1 (2014): 28--41
Keywords
- Modified intuitionistic fuzzy metric space
- weakly compatible mappings
- common limit range property
- fixed point.
MSC
References
-
[1]
M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. , 270(1) (2002), 181-188.
-
[2]
A. T. Atanassov , Intuitionistic fuzzy sets , Fuzzy Sets & Systems, 20 (1986), 87-96.
-
[3]
A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29(9) (2002), 531-536.
-
[4]
E. Canzoneri, P. Vetro, Fixed points for asymptotic contractions of integral Meir-Keeler type, J. Nonlinear Sci. Appl., 5(2) (2012), 126-132.
-
[5]
S. Chauhan, M. Imdad, B. Samet, Coincidence and Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces, Math. Comput. Model., in press. (2013)
-
[6]
S. Chauhan, B. D. Pant, S. Radenović, Common fixed point theorems for R-weakly commuting mappings with common limit in the range property, J. Indian Math. Soc., J. Indian Math. Soc. (2014), in press.
-
[7]
Y. J. Cho, B. E. Rhoades, R. Saadati, B. Samet, W. Shatanawi , Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type, Fixed Point Theory Appl. , Vol. 2012, Article 8 (2012)
-
[8]
Y. J. Cho, R. Saadati, A common fixed point theorem in intuitionistic fuzzy metric spaces, Int. J. Comput. Appl. Math., 2(1) (2007), 1-5.
-
[9]
G. Deschrijver, C. Cornelis, E. E. Kerre, On the representation of intuitionistic fuzzy t-norm and t-conorm, IEEE Trans. Fuzzy System, 12 (2004), 45-61.
-
[10]
G. Deschrijver, E. E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets & Systems, 133 (2003), 227-235.
-
[11]
A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl., 329(1) (2007), 31-45.
-
[12]
A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets & Systems, 64 (1994), 395-399.
-
[13]
V. Gregori, S. Romaguera, P. Veereamani, A note on intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 28 (2006), 902-905.
-
[14]
M. Imdad, J. Ali , Some common fixed point theorems in fuzzy metric spaces, Math. Commun., 11 (2006), 153-163.
-
[15]
M. Imdad, J. Ali, M. Hasan, Common fixed point theorems in modified intuitionistic fuzzy metric spaces, Iran. J. Fuzzy Syst., 9(5) (2012), 77-92.
-
[16]
M. Imdad, B. D. Pant, S. Chauhan, Fixed point theorems in Menger spaces using the (CLRST ) property and applications, J. Nonlinear Anal. Optim. Theory Appl., 3(2) (2012), 225-237.
-
[17]
S. Jain, S. Jain, L. B. Jain, Compatibility of type (P) in modified intuitionistic fuzzy metric space, J. Nonlinear Sci. Appl., 3(2) (2010), 96-109.
-
[18]
G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29(3) (1998), 227-238.
-
[19]
Y. Li, F. Gu, Common fixed point theorem of Altman integral type mappings, J. Nonlinear Sci. Appl., 2(4) (2009), 214-218.
-
[20]
Y. Liu, Jun Wu, Z. Li, Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci., 2005 (2005), 3045-3055.
-
[21]
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22 (2004), 1039-1046.
-
[22]
K. P. R. Rao, Md. Mustaq Ali, A. Som Babu, Common fixed points for D-maps satisfying integral type condition, J. Nonlinear Sci. Appl., 3(4) (2010), 294-301.
-
[23]
R. Saadati, S. Sedghi, N. Shobe, Modified Intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos, Solitons & Fractals, 38 (2008), 36-47.
-
[24]
B. Samet, C. Vetro, An integral version of Ćirić's fixed point theorem, Mediterr. J. Math., 9 (2012), 225-238.
-
[25]
S. Sedghi, N. Shobe, A. Aliouche, Common fixed point theorems in intuitionistic fuzzy metric spaces through conditions of integral type, Appl. Math. Inform. Sci., 2(1) (2008), 61-82.
-
[26]
W. Sintunavarat, S. Chauhan, P. Kumam, Some fixed point results in modified intuitionistic fuzzy metric spaces, Afrika Mat. DOI 10.1007/s13370-012-0128-0 , in press (2013)
-
[27]
W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., Article ID 637958, 2011 (2011), 14 pages.
-
[28]
T. Suzuki, Meir-Keeler contractions of integral type are still Meir-Keeler contractions, Int. J. Math. Math. Sci. Art. ID 39281, 2007 (2007), 6 pages.
-
[29]
M. Tanveer, M. Imdad, D. Gopal, D. K. Patel , Common fixed point theorems in modified intuitionistic fuzzy metric spaces with common property (E.A.) , Fixed Point Theory Appl., 2012 (2012), 36 pages.
-
[30]
C. Vetro , On Branciari's theorem for weakly compatible mappings, Appl. Math. Lett., 23(6) (2010), 700-705.
-
[31]
P. Vijayaraju, B. E. Rhoades, R. Mohanraj , A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Internat. J. Math. Math. Sci., 15 (2005), 2359-2364.