New fixed point theorem for \(\varphi\)-contractions in KM-fuzzy metric spaces
-
1639
Downloads
-
2438
Views
Authors
Jiaming Jin
- Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.
Chuanxi Zhu
- Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.
Haochen Wu
- Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.
Abstract
In this paper, by modifying the class of gauge functions \(\Phi_w\) and \(\Phi_{w^*}\) , a new fixed point theorem for
\(\varphi\)-contractions in KM-fuzzy metric spaces with a t-norm of H-type is established. We also give an example
to illustrate the validity of our main results.
Share and Cite
ISRP Style
Jiaming Jin, Chuanxi Zhu, Haochen Wu, New fixed point theorem for \(\varphi\)-contractions in KM-fuzzy metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 6204--6209
AMA Style
Jin Jiaming, Zhu Chuanxi, Wu Haochen, New fixed point theorem for \(\varphi\)-contractions in KM-fuzzy metric spaces. J. Nonlinear Sci. Appl. (2016); 9(12):6204--6209
Chicago/Turabian Style
Jin, Jiaming, Zhu, Chuanxi, Wu, Haochen. "New fixed point theorem for \(\varphi\)-contractions in KM-fuzzy metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 6204--6209
Keywords
- Fixed point
- Menger probabilistic metric space
- H-type
- \(\varphi\)-contraction.
MSC
References
-
[1]
D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458--464
-
[2]
L. Ćirić, Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces, Non- linear Anal., 72 (2010), 2009--2018
-
[3]
J.-X. Fang, On \(\varphi\)-contractions in probabilistic and fuzzy metric spaces, Fuzzy Sets Systems, 267 (2015), 86--99
-
[4]
O. Hadžić, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht (2001)
-
[5]
H. C. Hua, M. J. Chen, S. H. Wang, New result on fixed point theorems for \(\varphi\)-contractions in Menger spaces, Fixed Point Theory and Appl., 2015 (2015), 9 pages
-
[6]
J. Jachymsjki, On probabilistic \(\varphi\)-contractions on Menger spaces, Nonlinear Anal., 73 (2010), 2199--2203
-
[7]
I. Kramosil, J. Michálek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 336--344
-
[8]
D. Mihet, A class of contractions in fuzzy metrics spaces, Fuzzy Sets Systems, 161 (2010), 1131--1137
-
[9]
A. Roldán, J. Martínez-Moreno, C. Roldán, Tripled fixed point theorem in fuzzy metric spaces and applications, Fixed Point Theory and Appl., 2013 (2013), 13 pages