Multivariate contraction mapping principle in Menger probabilistic metric spaces
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Authors
Jinyu Guan
- Department of Mathematics, College of Science, Hebei North University, Zhangjiakou 075000, China.
Yanxia Tang
- Department of Mathematics, College of Science, Hebei North University, Zhangjiakou 075000, China.
Yongchun Xu
- Department of Mathematics, College of Science, Hebei North University, Zhangjiakou 075000, China.
Yongfu Su
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.
Abstract
The purpose of this paper is to prove the multivariate contraction mapping principle of \(N\)-variables mappings in Menger probabilistic metric spaces. In order to get the multivariate contraction mapping principle, the product spaces of Menger probabilistic metric spaces are subtly defined which is used as an important method for the expected results. Meanwhile, the relative iterative algorithm of the multivariate fixed point is established. The results of this paper improve and extend the contraction mapping principle of single variable mappings in the probabilistic metric spaces.
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ISRP Style
Jinyu Guan, Yanxia Tang, Yongchun Xu, Yongfu Su, Multivariate contraction mapping principle in Menger probabilistic metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4741--4750
AMA Style
Guan Jinyu, Tang Yanxia, Xu Yongchun, Su Yongfu, Multivariate contraction mapping principle in Menger probabilistic metric spaces. J. Nonlinear Sci. Appl. (2017); 10(9):4741--4750
Chicago/Turabian Style
Guan, Jinyu, Tang, Yanxia, Xu, Yongchun, Su, Yongfu. "Multivariate contraction mapping principle in Menger probabilistic metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4741--4750
Keywords
- Contraction mapping principle
- probabilistic metric spaces
- product spaces
- multivariate fixed point.
MSC
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