# Computational coupled fixed points for $\mathbf{F}$-contractive mappings in metric spaces endowed with a graph

Volume 16, Issue 3, pp 372-385
Publication Date: September 15, 2016 Submission Date: March 21, 2016
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### Authors

Phumin Sumalai - KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. Poom Kumam - KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. Dhananjay Gopal - Department of Applied Mathematics and Humanities, S. V. National Institute of Technology, Surat-395007, Gujarat, India.

### Abstract

The purpose of this work is to present some existence theorems for coupled fixed points of F-type 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.

### Share and Cite

##### ISRP Style

Phumin Sumalai, Poom Kumam, Dhananjay Gopal, Computational coupled fixed points for $\mathbf{F}$-contractive mappings in metric spaces endowed with a graph, Journal of Mathematics and Computer Science, 16 (2016), no. 3, 372-385

##### AMA Style

Sumalai Phumin, Kumam Poom, Gopal Dhananjay, Computational coupled fixed points for $\mathbf{F}$-contractive mappings in metric spaces endowed with a graph. J Math Comput SCI-JM. (2016); 16(3):372-385

##### Chicago/Turabian Style

Sumalai, Phumin, Kumam, Poom, Gopal, Dhananjay. "Computational coupled fixed points for $\mathbf{F}$-contractive mappings in metric spaces endowed with a graph." Journal of Mathematics and Computer Science, 16, no. 3 (2016): 372-385

### Keywords

• Coupled fixed point
• directed graph
• nonlinear integral equations.

•  47H10
•  54H25
•  05C40

### References

• [1] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393.

• [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), 1359-1373.

• [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.