Computational coupled fixed points for \(\mathbf{F}\)contractive mappings in metric spaces endowed with a graph

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Authors
Phumin Sumalai
 KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 PrachaUthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
Poom Kumam
 KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 PrachaUthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
Dhananjay Gopal
 Department of Applied Mathematics and Humanities, S. V. National Institute of Technology, Surat395007, Gujarat, India.
Abstract
The purpose of this work is to present some existence theorems for coupled fixed points of Ftype
contractive operator in metric spaces endowed with a directed graph. Our results generalize the main
result obtained by Chifu and Petrusel [C. Chifu, G. Petrusel, Fixed Point Theory Appl., 2014 (2014),
13 pages]. We also present applications to some nonlinear integral system equations to support the
results.
Keywords
 Coupled fixed point
 directed graph
 nonlinear integral equations.
MSC
References

[1]
T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 13791393.

[2]
C. Chifu, G. Petrusel, New results on coupled fixed point theory in metric spaces endowed with a directed graph , Fixed Point Theory Appl., 2014 (2014 ), 13 pages.

[3]
J. Jachymski , The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 13591373.

[4]
S. Suantai, P. Charoensawan, T. A. Lampert, Common coupled fixed point theorems for (\theta\psi\)contraction mappings endowed with a directed graph , Fixed Point Theory Appl., 2015 (2015 ), 11 pages.

[5]
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 6 pages.