Common fixed point theorems in Menger probabilistic metric spaces using the CLRg property
Volume 12, Issue 1, pp 48--55
http://dx.doi.org/10.22436/jnsa.012.01.05
Publication Date: October 10, 2018
Submission Date: October 07, 2017
Revision Date: August 05, 2018
Accteptance Date: August 17, 2018
-
1901
Downloads
-
3650
Views
Authors
Shuang Wang
- School of Mathematical Sciences, Yancheng Teachers University, Yancheng, 224051, Jiangsu, P. R. China.
Dingbian Qian
- School of Mathematical Sciences, Soochow University, Suzhou 215006, China.
Abstract
Under some weaker conditions of the \(\varphi\), some common fixed point theorems for weakly compatible mappings are established in Menger probabilistic metric spaces. Using the CLRg property, our results show that the completeness of underlying spaces is not necessary for fixed point theorems. In order to illustrate our results, we provide two examples in which other theorems cannot be applied.
Share and Cite
ISRP Style
Shuang Wang, Dingbian Qian, Common fixed point theorems in Menger probabilistic metric spaces using the CLRg property, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 1, 48--55
AMA Style
Wang Shuang, Qian Dingbian, Common fixed point theorems in Menger probabilistic metric spaces using the CLRg property. J. Nonlinear Sci. Appl. (2019); 12(1):48--55
Chicago/Turabian Style
Wang, Shuang, Qian, Dingbian. "Common fixed point theorems in Menger probabilistic metric spaces using the CLRg property." Journal of Nonlinear Sciences and Applications, 12, no. 1 (2019): 48--55
Keywords
- Menger probabilistic metric spaces
- weakly compatible mappings
- common fixed points
- common limit in the range property
MSC
References
-
[1]
M. Abbas, M. Ali Khan, S. Radenovic, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195–202.
-
[2]
L. Ćirić , Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces , Nonlinear Anal., 72 (2010), 2009–2018.
-
[3]
J.-X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833–1843.
-
[4]
J.-X. Fang, On \(\varphi\)-contractions in probabilistic and fuzzy metric spaces, Fuzzy Sets and Systems, 267 (2015), 86–99.
-
[5]
O. Hadžić, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht (2001)
-
[6]
X.-Q. Hu , Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces, Fixed Point Theory Appl., 2011 (2011), 14 pages.
-
[7]
X.-Q. Hu, M.-X. 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.
-
[8]
J. Jachymski, On probabilistic \(\phi\)-contractions on Menger spaces, Nonlinear Anal., 73 (2010), 2199–2203.
-
[9]
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.
-
[10]
K. Menger , Statistical metrics, Proc. Natl. Acad. Sci., 1942 (1942), 535–537.
-
[11]
D. O’Regan, R. Saadati , Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput., 195 (2008), 86–93.
-
[12]
A.-F. Roldn-Lpez-de-Hierro, W. Sintunavarat, Common fixed point theorems in fuzzy metric spaces using the CLRg property , Fuzzy Sets and Systems, 282 (2016), 131–142.
-
[13]
B. Schweizer, A. Sklar, Probabilistic Metric Spaces, Dover Publications, New York (2005)
-
[14]
V. M. Sehgal, A. T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric spaces, Math. Systems Theory, 6 (1972), 97–102.
-
[15]
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.