A unique coupled common fixed point theorem for symmetric \((\varphi,\psi)\)-contractive mappings in ordered \(G\)-metric spaces with applications (Q1789750)

Summary: We establish the existence and uniqueness of coupled common fixed point for symmetric \((\varphi,\psi)\)-contractive mappings in the framework of ordered \(G\)-metric spaces. Present work extends, generalize, and enrich the recent results of \textit{B. S. Choudhury} and \textit{P. Maity} [Math. Comput. Modelling 54, No. 1--2, 73--79 (2011; Zbl 1225.54016)], \textit{H. K. Nashine} [J. Nonlinear Sci. Appl. 5, No. 1, 1--13 (2012; Zbl 1295.54069)], and \textit{S. A. Mohiuddine} and \textit{A. Alotaibi} [Abstr. Appl. Anal. 2012, Article ID 897198, 15 p. (2012; Zbl 1296.54074)], thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.