Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using the CLRg property
-
1370
Downloads
-
2117
Views
Authors
Shuang Wang
- School of Mathematical Sciences, Yancheng Teachers University, Yancheng, 224051, Jiangsu, P. R. China.
Abstract
By means of weakening conditions of the gauge function \(\phi\) and the CLRg property, some common fixed
point theorems are established in fuzzy metric spaces. The two mappings considered here are assumed
to be weakly compatible. Our results extend and improve very recent theorems in the related literature.
Share and Cite
ISRP Style
Shuang Wang, Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using the CLRg property, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 1043--1051
AMA Style
Wang Shuang, Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using the CLRg property. J. Nonlinear Sci. Appl. (2016); 9(3):1043--1051
Chicago/Turabian Style
Wang, Shuang. "Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using the CLRg property." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 1043--1051
Keywords
- Fuzzy metric spaces
- weakly compatible mappings
- common fixed points
- common limit in the range property.
MSC
References
-
[1]
M. Aamri, D. E. Moutawakil , Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188.
-
[2]
M. Abbas, M. A. Khan, S. Radenovic , Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195-202.
-
[3]
L. Ćirić , Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces, Non-linear Anal., 72 (2010), 2009-2018.
-
[4]
J. X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833-1843.
-
[5]
J. X. Fang, On \(\varphi\)-contractions in probabilistic and fuzzy metric spaces, Fuzzy Sets and Systems, 267 (2015), 86-99.
-
[6]
A. Francisco, R. L. Hierroa, W. Sintunavarat, Common fixed point theorems in fuzzy metric spaces using the CLRg property, Fuzzy Sets and Systems, 282 (2014), 131-142.
-
[7]
A. George, P. Veeramani, On some result in fuzzy metric space, Fuzzy Sets and Systems, 64 (1994), 395-399.
-
[8]
T. Gnana-Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393.
-
[9]
M. Grabiec, Fixed points in fuzzy metric spaces , Fuzzy Sets and Systems, 27 (1988), 385-389.
-
[10]
V. Gregori, S. Morillas, A. Sapena, On a class of completable fuzzy metric spaces, Fuzzy Sets and Systems, 161 (2010), 2193-2205.
-
[11]
O. Hadžić, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht (2001)
-
[12]
X. Q. Hu, Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces, Fixed Point Theory Appl., 2011 (2011), 14 pages.
-
[13]
X. Q. Hu, M. Xue Zheng, B. Damjanović, X. F. Shao, Common coupled fixed point theorems for weakly compatible mappings in fuzzy metric spaces, Fixed Point Theory Appl., 2013 (2013), 11 pages.
-
[14]
M. Jain, K. Tas, S. Kumar, N. Gupta, Coupled fixed point theorems for a pair of weakly compatible maps along with CLRg property in fuzzy metric spaces, J. Appl. Math., 2012 (2012), 13 pages.
-
[15]
G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), 771-779.
-
[16]
G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227-238.
-
[17]
I. Kramosil, J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11 (1975), 336-344.
-
[18]
D. O'Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput., 195 (2008), 86-93.
-
[19]
K. P. R. Sastry, I. S. R. Krishna Murthy, Common fixed points of two partially commuting tangential selfmaps on a metric space, J. Math. Anal. Appl., 250 (2000), 731-734.
-
[20]
B. Schweizer, A. Sklar, Probabilistic Metric Spaces, Dover Publications, NewYork (2005)
-
[21]
S. Sessa, On a weak commutativity condition in fixed point considerations, Publ. Inst. Math., 34 (1982), 149-153.
-
[22]
W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011 (2011), 14 pages.