Document Type : Research Paper


1 Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 Young Researchers and Elite club, West Tehran Branch, Islamic Azad University, Tehran, Iran


In this paper, we apply the idea of integral type contraction and prove some coupled fixed point theorems for such contractions in ordered $G$-metric space. Also, we support the main results by an illustrative example.


Main Subjects

[1] R. P. Agarwal, M. A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8.
[2] P. R. Agarwal, Z. Kadelburg, S. Radenovic, On coupled fixed point results in asymmetric G-metric spaces, Journal of Inequalities and Applications. (2013), 2013:528.
[3] R. P. Agarwal, E. Karapinar, D. O’Regan, A. F. Roldan-López-de-Hierro, Fixed Point Theory in Metric Type Spaces, Springer, Switzerland, 2015.
[4] A. Aghanians, K. Nourouzi, Fixed points of integral type contractions in uniform spaces, Filomat. 29 (7) (2015), 1613-1621.
[5] R. Akbar Zada, T. Li, Integral type contraction and coupled coincidence fixed point theorems for two pairs in G-metric spaces, Hecet. J. Math. Stat. 45 (5) (2016), 1475-1484.
[6] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393.
[7] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Inter. J. Math. Sci. 29 (2002), 531-536.
[8] D. J. Guo, Partial Order Methods in Nonlinear Analysis, Shandong Sci. Technol. Press, Jinan, 2000  (in Chinese).
[9] J. Harjani, B. López, K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 (2011), 1749-1760.
[10] M. Jleli, B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory Appl. (2012), 2012:210.
[11] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2) (2006), 289-297.
[12] J. J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order. 22 (2005), 223-239.
[13] S. Radenovic, Bhaskar-Lakshmikantham type-results for monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl. 5 (2) (2014), 37-49.
[14] S. Radenovic, Coupled fixed point theorems for monotone mappings in partially ordered metric spaces, Kragujevac J. Math. 38 (2) (2014), 249-257.
[15] 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.
[16] B. Samet, C. Vetro, An integral version of´Ciri´ c’s fixed point theorem, Mediterr. J. Math. 9 (1) (2012), 225-238.
[17] B. Samet, C.Vetro, F.Vetro, Remarks on G-Metric spaces, Inter. J. Anal. (2013), 2013:917158.
[18] G. Soleimani Rad, S. Shukla, H. Rahimi, Some relations between n-tuple fixed point and fixed point results, RACSAM. 109 (2015), 471-481.