Multivariate best proximity point theorems in metric spaces
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Authors
Yinglin Luo
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.
Yongfu Su
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.
Wenbiao Gao
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.
Abstract
The purpose of this paper is to prove an existence and uniqueness theorems of the multivariate best
proximity point in the complete metric spaces. The concept of multivariate best proximity point is firstly
introduced in this article. These new results improve and extend the previously known ones in the literature.
Share and Cite
ISRP Style
Yinglin Luo, Yongfu Su, Wenbiao Gao, Multivariate best proximity point theorems in metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 11, 5756--5765
AMA Style
Luo Yinglin, Su Yongfu, Gao Wenbiao, Multivariate best proximity point theorems in metric spaces. J. Nonlinear Sci. Appl. (2016); 9(11):5756--5765
Chicago/Turabian Style
Luo, Yinglin, Su, Yongfu, Gao, Wenbiao. "Multivariate best proximity point theorems in metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 11 (2016): 5756--5765
Keywords
- Contraction mapping principle
- complete metric spaces
- multivariate mapping
- multivariate fixed point
- multiply metric function
- best proximity point theorem.
MSC
References
-
[1]
A. Amini-Harandi, N. Hussain, F. Akbar, Best proximity point results for generalized contractions in metric spaces, Fixed Point Theory and Appl., 2013 (2013), 13 pages
-
[2]
K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math Z., 112 (1969), 234--240
-
[3]
E. Karapınar, On best proximity point of \(\psi\) -Geraghty contractions, Fixed Point Theory and Appl., 2013 (2013), 9 pages
-
[4]
C. Mongkolkeha, Y. J. Cho, P. Kumam, Best proximity points for Geraghty's proximal contraction mappings, Fixed Point Theory and Appl., 2013 (2013), 17 pages
-
[5]
H. K. Nashine, P. Kumam, C. Vetro, Best proximity point theorems for rational proximal contractions, Fixed Point Theory and Appl., 2013 (2013), 11 pages
-
[6]
S. Sadiq Basha, Best proximity point theorems generalizing the contraction principle, Nonlinear Anal., 74 (2011), 5844--5850
-
[7]
Y. F. Su, A. Petruşel, J.-C. Yao, Multivariate fixed point theorems for contractions and nonexpansive mappings with applications, Fixed Point Theory and Appl., 2016 (2016), 19 pages
-
[8]
Y. F. Su, J.-C. Yao, Further generalized contraction mapping principle and best proximity theorem in metric spaces, Fixed Point Theory and Appl., 2015 (2015), 13 pages
-
[9]
F. F. Yan, Y. F. Su, Q. S. Feng, A new contraction mapping principle in partially ordered metric spaces and applications to ordinary difierential equations, Fixed Point Theory and Appl., 2012 (2012), 13 pages
-
[10]
J. L. Zhang, Y. F. Su, Best proximity point theorems for weakly contractive mapping and weakly Kannan mapping in partial metric spaces, Fixed Point Theory and Appl., 2014 (2014), 8 pages
-
[11]
J. L. Zhang, Y. F. Su, Q. Q. Cheng, A note on 'A best proximity point theorem for Geraghty-contractions', Fixed Point Theory and Appl., 2013 (2013), 4 pages
-
[12]
J. L. Zhang, Y. F. Su, Q. Q. Cheng, Best proximity point theorems for generalized contractions in partially ordered metric spaces, Fixed Point Theory and Appl., 2013 (2013), 7 pages