A note on coincidence points of multivalued weak G-contraction mappings
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Authors
Monther Rashed Alfuraidan
- Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
Mohamed Amine Khamsi
- Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, U. S. A..
Abstract
In this note, we discuss the definition of the multivalued weak contraction mappings defined in a metric
space endowed with a graph as introduced by Hanjing and Suantai[A. Hanjing, S. Suantai, Fixed Point
Theory Appl., 2015 (2015), 10 pages]. In particular, we show that this definition is not correct and give the
correct definition of the multivalued weak contraction mappings defined in a metric space endowed with a
graph. Then we prove the existence of coincidence points for such mappings.
Share and Cite
ISRP Style
Monther Rashed Alfuraidan, Mohamed Amine Khamsi, A note on coincidence points of multivalued weak G-contraction mappings, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4098--4103
AMA Style
Alfuraidan Monther Rashed, Khamsi Mohamed Amine, A note on coincidence points of multivalued weak G-contraction mappings. J. Nonlinear Sci. Appl. (2016); 9(6):4098--4103
Chicago/Turabian Style
Alfuraidan, Monther Rashed, Khamsi, Mohamed Amine. "A note on coincidence points of multivalued weak G-contraction mappings." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4098--4103
Keywords
- Directed graph
- coincidence points
- weak G-contraction mappings
- Reich multivalued mapping.
MSC
References
-
[1]
M. R. Alfuraidan, Remarks on monotone multivalued mappings on a metric space with a graph, J. Ineq. Appl., 2015 (2015), 7 pages.
-
[2]
I. Beg, A. R. Butt, Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal., 71 (2009), 3699-3704.
-
[3]
M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl., 326 (2007), 772-782.
-
[4]
M. Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc., 12 (1961), 7-10.
-
[5]
W-S. Du, On coincidence point and fixed point theorems for nonlinear multivalued maps, Topol. Appl., 159 (2012), 49-56.
-
[6]
Y. Feng, S. Liu , Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings, J. Math. Anal. Appl., 317 (2006), 103-112.
-
[7]
A. Hanjing, S. Suantai, Coincidence point and fixed point theorems for a new type of G-contraction multivalued mappings on a metric space endowed with a graph, Fixed Point Theory Appl., 2015 (2015), 10 pages.
-
[8]
D. Klim, D. Wardowski , Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334 (2007), 132-139.
-
[9]
N. Mizoguchi, W. Takahashi , Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl., 141 (1989), 177-188.
-
[10]
S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488.
-
[11]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.